第5章 二次根式单元检测A卷
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21世纪教育网 –中小学教育资源及组卷应用平台
二次根式单元检测A卷
姓名：__________班级：__________学号：__________
1 、选择题（本大题共12小题）
根式 ( http: / / www.21cnjy.com / )的值是（ ）
A． ﹣3 B． 3 C． 3或﹣3 D． 9
下列各式中，为二次根式的是（ ）
A． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/0.png" \* MERGEFORMATINET B． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/1.png" \* MERGEFORMATINET C． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/2.png" \* MERGEFORMATINET D． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/3.png" \* MERGEFORMATINET
式子 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/0.png" \* MERGEFORMATINET 、 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/1.png" \* MERGEFORMATINET 、 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/2.png" \* MERGEFORMATINET 、 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/3.png" \* MERGEFORMATINET 中，有意义的式子个数为（ ）
A．1个 B．2个 C．3个 D．4个
下列根式中，不是最简二次根式的是（ ）
A． ( http: / / www.21cnjy.com ) B． ( http: / / www.21cnjy.com ) C． ( http: / / www.21cnjy.com ) D． ( http: / / www.21cnjy.com )
的结果是（ ）
A． B． C． INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/3.png" \* MERGEFORMATINET D． INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/4.png" \* MERGEFORMATINET 21教育名师原创作品
( http: / / www.21cnjy.com )的倒数是（ ）
A． ( http: / / www.21cnjy.com ) B． ( http: / / www.21cnjy.com ) C．﹣3 D． ( http: / / www.21cnjy.com )
下列各组二次根式中是同类二次根式的是（ ）
A． ( http: / / www.21cnjy.com ) B． ( http: / / www.21cnjy.com ) C． ( http: / / www.21cnjy.com ) D． ( http: / / www.21cnjy.com )
计算 ( http: / / www.21cnjy.com )的结果是（ ）
A．3 B． ( http: / / www.21cnjy.com ) C．2 ( http: / / www.21cnjy.com ) D． ( http: / / www.21cnjy.com )
下列运算正确的是（ ）
A．﹣a a3=a3 B．﹣（a2）2=a4 C．x﹣ ( http: / / www.21cnjy.com )x= ( http: / / www.21cnjy.com ) D．（ ( http: / / www.21cnjy.com )﹣2）（ ( http: / / www.21cnjy.com )+2）=﹣1
式子 ( http: / / www.21cnjy.com )在实数范围内有意义，则x的取值范围是（ ）
A．x＜1 B．x≤1 C．x＞1 D．x≥1
化简 ( http: / / www.21cnjy.com / )﹣（ ( http: / / www.21cnjy.com / )）2，结果是（ ）
A．6x﹣6 B．﹣6x+6 C．﹣4 D．4
如果一个三角形的三边长分别为1、k、4．则化简|2k﹣5|﹣ ( http: / / www.21cnjy.com )的结果是（ ）
A．3k﹣11 B．k+1 C．1 D．11﹣3k
1 、填空题（本大题共8小题）
代数式 INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_ST/0.png" \* MERGEFORMATINET 的最大值为 ，此时x= ．
若x＜2，化简 ( http: / / www.21cnjy.com )+|3﹣x|的正确结果是 ．
若一个矩形的长为 ( http: / / www.21cnjy.com / )cm，宽为 ( http: / / www.21cnjy.com / )cm，则与它面积相等的正方形的边长为 cm．
16. 计算 QUOTE http://www.21cnjy.com/ ( http: / / www.21cnjy.com ) 的结果是_______.
当 ( http: / / www.21cnjy.com )= 时，两个最简二次根式和可以合并.
化简： ( http: / / www.21cnjy.com ) = ．
已知，则 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_ST/1.png" \* MERGEFORMATINET =______．
已知：x=，y=，那么x2+y2的值为 ．
1 、解答题（本大题共8小题）
已知，，求（1）+的值；（2）的值；（3）的值.
计算下列各题：
（1）； （2）；
（3）； （4）；
（5）．
计算：
（1）9 ( http: / / www.21cnjy.com )﹣7 ( http: / / www.21cnjy.com )+5 ( http: / / www.21cnjy.com )； （2） ( http: / / www.21cnjy.com )÷ ( http: / / www.21cnjy.com )﹣ ( http: / / www.21cnjy.com )× ( http: / / www.21cnjy.com )+ ( http: / / www.21cnjy.com )．
已知a，b是有理数，若 ( http: / / www.21cnjy.com )+2 ( http: / / www.21cnjy.com )=b+4，求a和b的值．
数a、b在数轴上的位置如图所示，化简：
. ( http: / / www.21cnjy.com )
已知 INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/0.png" \* MERGEFORMATINET ，求 INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/1.png" \* MERGEFORMATINET 的值．
已知三角形的两边长分别为3和5，第三边长为c，化简 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_ST/0.png" \* MERGEFORMATINET ．
如图是一个正方体展开图，已知正方体相对 ( http: / / www.21cnjy.com )两面的代数式的值相等；
（1）求a、b、c 的值；
（2）判断a+b-c的平方根是有理数还是无理数．21世纪教育网版权所有
答案解析
1 、选择题
【分析】 根据二次根式的性质： ( http: / / www.21cnjy.com / )=|a|进行化简，然后再去绝对值即可．
解： ( http: / / www.21cnjy.com / )=|﹣3|=﹣（﹣3）=3．
故选B．
【分析】根据二次根式的性质，被开方数大于 ( http: / / www.21cnjy.com )或等于0可知．
解：、被开方数是负数，根式无意义，不是二次根式；
B、是三次根式，不是二次根式；
C、被开方数是负数，根式无意义，不是二次根式；
D、被开方数是非负数，是二次根式．
故选D．21·cn·jy·com
【分析】根据二次根式的有意义的条件，逐一判断．
解： INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/0.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/1.png" \* MERGEFORMATINET 与 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/2.png" \* MERGEFORMATINET 的被开方数小于0，没有意义；
INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/3.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/4.png" \* MERGEFORMATINET 与 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/5.png" \* MERGEFORMATINET 的被开方数大于等于0，有意义．
故有意义的式子有2个．
故选B．【来源：21·世纪·教育·网】
【分析】判定一个二次根式是不是最简二次根 ( http: / / www.21cnjy.com )式的方法，就是逐个检查最简二次根式中的两个条件（被开方数不含分母，也不含能开的尽方的因数或因式）．是否同时满足，同时满足的就是最简二次根式，否则就不是．21教育网2-1-c-n-j-y
解：因为 ( http: / / www.21cnjy.com )= ( http: / / www.21cnjy.com )=2 ( http: / / www.21cnjy.com )，因此 ( http: / / www.21cnjy.com )不是最简二次根式．
故选B．
【分析】根据负整数指数幂的运算法则进行计算，再分母有理化．
解：原式= INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/0.png" \* MERGEFORMATINET
= INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/1.png" \* MERGEFORMATINET
=-1- INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/2.png" \* MERGEFORMATINET ．
故选D．21*cnjy*com
【分析】利用倒数定义得到结果，化简即可．
解： ( http: / / www.21cnjy.com )的倒数为 ( http: / / www.21cnjy.com )= ( http: / / www.21cnjy.com )．
故选D
【分析】化简各选项后根据同类二次根式的定义判断．
解：A． ( http: / / www.21cnjy.com )=2 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数不同，故不是同类二次根式，故A选项错误；
B、 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数不同，故不是同类二次根式，故B选项错误；
C、 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数相同，是同类二次根式，故C选项正确；
D、 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数不同，故不是同类二次根式，故D选项错误．
故选：C．
【分析】把 ( http: / / www.21cnjy.com )化简为2 ( http: / / www.21cnjy.com )，再和﹣ ( http: / / www.21cnjy.com )合并即可得问题答案．
解：原式= ( http: / / www.21cnjy.com )，
=2 ( http: / / www.21cnjy.com )﹣ ( http: / / www.21cnjy.com )，
= ( http: / / www.21cnjy.com )．
故选B．
【分析】利用同底数的幂的乘法法则、幂的乘方、合并同类项法则，以及平方差公式即可判断．
解：A．﹣a a3=﹣a4，故选项错误；
B、﹣（a2）2=﹣a4，选项错误；
C、x﹣ ( http: / / www.21cnjy.com )x= ( http: / / www.21cnjy.com )x，选项错误；
D、（ ( http: / / www.21cnjy.com )﹣2）（ ( http: / / www.21cnjy.com )+2）=（ ( http: / / www.21cnjy.com )）2﹣22=3﹣4=﹣1，选项正确．
故选D．
【分析】被开方数是非负数，且分母不为零，由此得到：x﹣1＞0，据此求得x的取值范围．
解：依题意得：x﹣1＞0，
解得x＞1．
故选：C．
【分析】求值的第一个式子是个完全平方公式，开方要注意正负值，由已知条件可得3x﹣5≥0，即3x≥5，所以3x﹣1＞0，据此求解． 2·1·c·n·j·y
解：由已知条件可得3x﹣5≥0，即3x≥5，则3x﹣1＞0，
∴原式= ( http: / / www.21cnjy.com / )（ ( http: / / www.21cnjy.com / )）2=3x﹣1﹣（3x﹣5）=3x﹣1﹣3x+5=4．
故选D．
【分析】由于三角形的三边 ( http: / / www.21cnjy.com )长分别为1、k、4，根据三角形的三边关系，1+4＞k，即k＜5，4﹣1＜k，所以k＞3，根据k的取值范围，再对代数式进行化简．www-2-1-cnjy-com
解：∵三角形的三边长分别为1、k、4，
∴ ( http: / / www.21cnjy.com )，
解得，3＜k＜5，
所以，2k﹣5＞0，k﹣6＜0，
∴|2k﹣5|﹣ ( http: / / www.21cnjy.com )=2k﹣5﹣ ( http: / / www.21cnjy.com )=2k﹣5﹣[﹣（k﹣6）]=3k﹣11．
故选A．
1 、填空题
【分析】根据算术平方根的性质可以得到 INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/0.png" \* MERGEFORMATINET ≥0，即最小值是0，据此即可确定原式的最大值．
解： INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/1.png" \* MERGEFORMATINET ≥0，
∴当x=±2时，有最小值0，
则当x=±2，3- INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/2.png" \* MERGEFORMATINET 有最大值是3．
故答案是：3，±2．21cnjy.com
【分析】先根据x的取值范围，判断出x﹣2和3﹣x的符号，然后再将原式进行化简．
解：∵x＜2，
∴x﹣2＜0，3﹣x＞0；
∴ ( http: / / www.21cnjy.com )+|3﹣x|=﹣（x﹣2）+（3﹣x）
=﹣x+2+3﹣x=5﹣2x．
【分析】先求出长方形的面积，再根据正方形的面积公式即可求得其边长．
解：长为 ( http: / / www.21cnjy.com / )cm，宽为 ( http: / / www.21cnjy.com / )cm的矩形的面积是 ( http: / / www.21cnjy.com / )× ( http: / / www.21cnjy.com / )=16cm2，
所以正方形的面积是16cm2，所以这个正方形的边长为 ( http: / / www.21cnjy.com / )=4cm．
故答案为：4．www.21-cn-jy.com
【分析】直接相乘化简后即可得出答案
解：.
【分析】 根据同类二次根式的定义求解
解：由题意知：2+1=2+，
解得=1.
因此当=1 QUOTE http://www.21cnjy.com/ ( http: / / www.21cnjy.com ) 时两最简二次根式可以合并.
【分析】先进行二次根式的化简，然后合并即可．
解：原式=3+2 ( http: / / www.21cnjy.com )+ ( http: / / www.21cnjy.com )
= ( http: / / www.21cnjy.com )．
【分析】根据二次根式有意义的条件，得2x-1=0，x= INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/0.png" \* MERGEFORMATINET ，然后求得y的值，最后代入 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/1.png" \* MERGEFORMATINET 求解．
解：二次根式有意义，则 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/2.png" \* MERGEFORMATINET ，
解得x= INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/3.png" \* MERGEFORMATINET ．
∴y==4．
∴==3．21教育网
【分析】将x、y的值化简，分别求出x+y、xy的值，根据x2+y2=（x+y）2-2xy求解．
解：∵x==-，y==+，
∴x+y=2，xy=1，
∴x2+y2=（x+y）2-2xy=（2）2-2=10．
故本题答案为10．【来源：21cnj*y.co*m】
1 、解答题
【分析】二次根式的加减，首先要把各项化为最简二次根式，是同类二次根式的才能合并，不是同类二次根式的不合并 21·世纪*教育网
解：（1） ( http: / / www.21cnjy.com / )+ ( http: / / www.21cnjy.com / )= + =-1+ 8=7
（2）;
（3） INCLUDEPICTURE "http://img./STSource/2014/06/27/18/ea7bdb3d/SYS201406271859418665271334_DA/SYS201406271859418665271334_DA.010.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/06/27/18/ea7bdb3d/SYS201406271859418665271334_DA/SYS201406271859418665271334_DA.010.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/06/27/18/ea7bdb3d/SYS201406271859418665271334_DA/SYS201406271859418665271334_DA.010.png" \* MERGEFORMATINET .
【分析】（1）分母是3 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/0.png" \* MERGEFORMATINET ，先化成最简二次根式，再分子、分母同乘以
（2）分子、分母同乘以 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/2.png" \* MERGEFORMATINET ；
（3）分子、分母同乘以 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/4.png" \* MERGEFORMATINET ；
（4）分子x-y可以分解成 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/5.png" \* MERGEFORMATINET ；后，直接与分母约分，从而化去分母；
（5）分子、分母分别分解因式，然后约分．
解：（1） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/6.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/6.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/6.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/7.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/7.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/7.png" \* MERGEFORMATINET ；
（2） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/8.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/8.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/8.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/9.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/9.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/9.png" \* MERGEFORMATINET ；
（3） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/10.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/10.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/10.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/11.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/11.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/11.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/12.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/12.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/12.png" \* MERGEFORMATINET ；
（4） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/13.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/13.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/13.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/14.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/14.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/14.png" \* MERGEFORMATINET ；
（5） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/15.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/15.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/15.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/16.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/16.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/16.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/17.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/17.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/17.png" \* MERGEFORMATINET ．
【分析】（1）先把各二次根式化为最简二次根式，然后合并即可；
（2）先利用二次根式的除法和乘法法则运算，然后合并即可．
解：（1）原式=9 ( http: / / www.21cnjy.com )﹣14 ( http: / / www.21cnjy.com )+20 ( http: / / www.21cnjy.com )
=15 ( http: / / www.21cnjy.com )；
（2）原式= ( http: / / www.21cnjy.com )﹣ ( http: / / www.21cnjy.com )+2 ( http: / / www.21cnjy.com )
=4﹣ ( http: / / www.21cnjy.com )+2 ( http: / / www.21cnjy.com )
=4+ ( http: / / www.21cnjy.com )．
【分析】根据二次根式的被开方数是非负数即可求得a的值，进而求得b的值．
解：根据题意得： ( http: / / www.21cnjy.com )，
解得：a=5，
则b+4=0，解得：b=﹣4．
【分析】利用二次根式的性质化简即可
解：由题意得
原式=-a-1+b-1-(b-a)
=-2
【分析】可先把原式化简再代入计算，主要是根据被开方数底数的符号开平方．
解：
=
=
=
=1．【出处：21教育名师】
【分析】由三边关系定理，得到关系式；判断出被开方数的正负，再化简开方，得出结果．
解：由三边关系定理，得3+5＞c，5-3＜c，即8＞c＞2，
INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/0.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/1.png" \* MERGEFORMATINET
=c-2-（4- INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/2.png" \* MERGEFORMATINET c）=c-2-4+ INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/3.png" \* MERGEFORMATINET c= INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/4.png" \* MERGEFORMATINET c-6．【版权所有：21教育】
【分析】（1）根据正方体相对两面的代数式的值相等可列出方程组，从而解出即可得出答案．
（2）根据（1）的结果，将各组数据分别代入可判断出结果．
解：1）依题意，得 INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/0.png" \* MERGEFORMATINET ，
由 ①、②得方程组： INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/1.png" \* MERGEFORMATINET ，
解得： INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/2.png" \* MERGEFORMATINET ，
由③得：c=±2，
∴a=3，b=1，c=±2．
（2）当a=3，b=1，c=-2 时
a+b-c=3+1+2=6，
a=3，b=1，c=2时
a+b-c=3+1-2=2，
∵和都是无理数
∴a+b-c 的平方根是无理数．21*cnjy*com
( http: / / www.21cnjy.com / )
HYPERLINK "http://www.21cnjy.com/" 版权所有@21世纪教育网(www.21cnjy.com)
二次根式单元检测A卷
姓名：__________班级：__________学号：__________
1 、选择题（本大题共12小题）
根式 ( http: / / www.21cnjy.com / )的值是（ ）
A． ﹣3 B． 3 C． 3或﹣3 D． 9
下列各式中，为二次根式的是（ ）
A． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/0.png" \* MERGEFORMATINET B． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/1.png" \* MERGEFORMATINET C． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/2.png" \* MERGEFORMATINET D． INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/11/d1fc7b3a/SYS201404291140146909057000_ST/3.png" \* MERGEFORMATINET
式子 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/0.png" \* MERGEFORMATINET 、 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/1.png" \* MERGEFORMATINET 、 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/2.png" \* MERGEFORMATINET 、 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_ST/3.png" \* MERGEFORMATINET 中，有意义的式子个数为（ ）
A．1个 B．2个 C．3个 D．4个
下列根式中，不是最简二次根式的是（ ）
A． ( http: / / www.21cnjy.com ) B． ( http: / / www.21cnjy.com ) C． ( http: / / www.21cnjy.com ) D． ( http: / / www.21cnjy.com )
的结果是（ ）
A． B． C． INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/3.png" \* MERGEFORMATINET D． INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_ST/4.png" \* MERGEFORMATINET 21教育名师原创作品
( http: / / www.21cnjy.com )的倒数是（ ）
A． ( http: / / www.21cnjy.com ) B． ( http: / / www.21cnjy.com ) C．﹣3 D． ( http: / / www.21cnjy.com )
下列各组二次根式中是同类二次根式的是（ ）
A． ( http: / / www.21cnjy.com ) B． ( http: / / www.21cnjy.com ) C． ( http: / / www.21cnjy.com ) D． ( http: / / www.21cnjy.com )
计算 ( http: / / www.21cnjy.com )的结果是（ ）
A．3 B． ( http: / / www.21cnjy.com ) C．2 ( http: / / www.21cnjy.com ) D． ( http: / / www.21cnjy.com )
下列运算正确的是（ ）
A．﹣a a3=a3 B．﹣（a2）2=a4 C．x﹣ ( http: / / www.21cnjy.com )x= ( http: / / www.21cnjy.com ) D．（ ( http: / / www.21cnjy.com )﹣2）（ ( http: / / www.21cnjy.com )+2）=﹣1
式子 ( http: / / www.21cnjy.com )在实数范围内有意义，则x的取值范围是（ ）
A．x＜1 B．x≤1 C．x＞1 D．x≥1
化简 ( http: / / www.21cnjy.com / )﹣（ ( http: / / www.21cnjy.com / )）2，结果是（ ）
A．6x﹣6 B．﹣6x+6 C．﹣4 D．4
如果一个三角形的三边长分别为1、k、4．则化简|2k﹣5|﹣ ( http: / / www.21cnjy.com )的结果是（ ）
A．3k﹣11 B．k+1 C．1 D．11﹣3k
1 、填空题（本大题共8小题）
代数式 INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_ST/0.png" \* MERGEFORMATINET 的最大值为 ，此时x= ．
若x＜2，化简 ( http: / / www.21cnjy.com )+|3﹣x|的正确结果是 ．
若一个矩形的长为 ( http: / / www.21cnjy.com / )cm，宽为 ( http: / / www.21cnjy.com / )cm，则与它面积相等的正方形的边长为 cm．
16. 计算 QUOTE http://www.21cnjy.com/ ( http: / / www.21cnjy.com ) 的结果是_______.
当 ( http: / / www.21cnjy.com )= 时，两个最简二次根式和可以合并.
化简： ( http: / / www.21cnjy.com ) = ．
已知，则 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_ST/1.png" \* MERGEFORMATINET =______．
已知：x=，y=，那么x2+y2的值为 ．
1 、解答题（本大题共8小题）
已知，，求（1）+的值；（2）的值；（3）的值.
计算下列各题：
（1）； （2）；
（3）； （4）；
（5）．
计算：
（1）9 ( http: / / www.21cnjy.com )﹣7 ( http: / / www.21cnjy.com )+5 ( http: / / www.21cnjy.com )； （2） ( http: / / www.21cnjy.com )÷ ( http: / / www.21cnjy.com )﹣ ( http: / / www.21cnjy.com )× ( http: / / www.21cnjy.com )+ ( http: / / www.21cnjy.com )．
已知a，b是有理数，若 ( http: / / www.21cnjy.com )+2 ( http: / / www.21cnjy.com )=b+4，求a和b的值．
数a、b在数轴上的位置如图所示，化简：
. ( http: / / www.21cnjy.com )
已知 INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/0.png" \* MERGEFORMATINET ，求 INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/1354c792/SYS201405141152590444392020_ST/1.png" \* MERGEFORMATINET 的值．
已知三角形的两边长分别为3和5，第三边长为c，化简 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_ST/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_ST/0.png" \* MERGEFORMATINET ．
如图是一个正方体展开图，已知正方体相对 ( http: / / www.21cnjy.com )两面的代数式的值相等；
（1）求a、b、c 的值；
（2）判断a+b-c的平方根是有理数还是无理数．21世纪教育网版权所有
答案解析
1 、选择题
【分析】 根据二次根式的性质： ( http: / / www.21cnjy.com / )=|a|进行化简，然后再去绝对值即可．
解： ( http: / / www.21cnjy.com / )=|﹣3|=﹣（﹣3）=3．
故选B．
【分析】根据二次根式的性质，被开方数大于 ( http: / / www.21cnjy.com )或等于0可知．
解：、被开方数是负数，根式无意义，不是二次根式；
B、是三次根式，不是二次根式；
C、被开方数是负数，根式无意义，不是二次根式；
D、被开方数是非负数，是二次根式．
故选D．21·cn·jy·com
【分析】根据二次根式的有意义的条件，逐一判断．
解： INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/0.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/1.png" \* MERGEFORMATINET 与 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/2.png" \* MERGEFORMATINET 的被开方数小于0，没有意义；
INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/3.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/4.png" \* MERGEFORMATINET 与 INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/01/22/09/c2b76717/SYS201401220927296981158012_DA/5.png" \* MERGEFORMATINET 的被开方数大于等于0，有意义．
故有意义的式子有2个．
故选B．【来源：21·世纪·教育·网】
【分析】判定一个二次根式是不是最简二次根 ( http: / / www.21cnjy.com )式的方法，就是逐个检查最简二次根式中的两个条件（被开方数不含分母，也不含能开的尽方的因数或因式）．是否同时满足，同时满足的就是最简二次根式，否则就不是．21教育网2-1-c-n-j-y
解：因为 ( http: / / www.21cnjy.com )= ( http: / / www.21cnjy.com )=2 ( http: / / www.21cnjy.com )，因此 ( http: / / www.21cnjy.com )不是最简二次根式．
故选B．
【分析】根据负整数指数幂的运算法则进行计算，再分母有理化．
解：原式= INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/0.png" \* MERGEFORMATINET
= INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/1.png" \* MERGEFORMATINET
=-1- INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/11/eed8ec2b/SYS201405141158575981859025_DA/2.png" \* MERGEFORMATINET ．
故选D．21*cnjy*com
【分析】利用倒数定义得到结果，化简即可．
解： ( http: / / www.21cnjy.com )的倒数为 ( http: / / www.21cnjy.com )= ( http: / / www.21cnjy.com )．
故选D
【分析】化简各选项后根据同类二次根式的定义判断．
解：A． ( http: / / www.21cnjy.com )=2 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数不同，故不是同类二次根式，故A选项错误；
B、 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数不同，故不是同类二次根式，故B选项错误；
C、 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数相同，是同类二次根式，故C选项正确；
D、 ( http: / / www.21cnjy.com )与 ( http: / / www.21cnjy.com )被开方数不同，故不是同类二次根式，故D选项错误．
故选：C．
【分析】把 ( http: / / www.21cnjy.com )化简为2 ( http: / / www.21cnjy.com )，再和﹣ ( http: / / www.21cnjy.com )合并即可得问题答案．
解：原式= ( http: / / www.21cnjy.com )，
=2 ( http: / / www.21cnjy.com )﹣ ( http: / / www.21cnjy.com )，
= ( http: / / www.21cnjy.com )．
故选B．
【分析】利用同底数的幂的乘法法则、幂的乘方、合并同类项法则，以及平方差公式即可判断．
解：A．﹣a a3=﹣a4，故选项错误；
B、﹣（a2）2=﹣a4，选项错误；
C、x﹣ ( http: / / www.21cnjy.com )x= ( http: / / www.21cnjy.com )x，选项错误；
D、（ ( http: / / www.21cnjy.com )﹣2）（ ( http: / / www.21cnjy.com )+2）=（ ( http: / / www.21cnjy.com )）2﹣22=3﹣4=﹣1，选项正确．
故选D．
【分析】被开方数是非负数，且分母不为零，由此得到：x﹣1＞0，据此求得x的取值范围．
解：依题意得：x﹣1＞0，
解得x＞1．
故选：C．
【分析】求值的第一个式子是个完全平方公式，开方要注意正负值，由已知条件可得3x﹣5≥0，即3x≥5，所以3x﹣1＞0，据此求解． 2·1·c·n·j·y
解：由已知条件可得3x﹣5≥0，即3x≥5，则3x﹣1＞0，
∴原式= ( http: / / www.21cnjy.com / )（ ( http: / / www.21cnjy.com / )）2=3x﹣1﹣（3x﹣5）=3x﹣1﹣3x+5=4．
故选D．
【分析】由于三角形的三边 ( http: / / www.21cnjy.com )长分别为1、k、4，根据三角形的三边关系，1+4＞k，即k＜5，4﹣1＜k，所以k＞3，根据k的取值范围，再对代数式进行化简．www-2-1-cnjy-com
解：∵三角形的三边长分别为1、k、4，
∴ ( http: / / www.21cnjy.com )，
解得，3＜k＜5，
所以，2k﹣5＞0，k﹣6＜0，
∴|2k﹣5|﹣ ( http: / / www.21cnjy.com )=2k﹣5﹣ ( http: / / www.21cnjy.com )=2k﹣5﹣[﹣（k﹣6）]=3k﹣11．
故选A．
1 、填空题
【分析】根据算术平方根的性质可以得到 INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/0.png" \* MERGEFORMATINET ≥0，即最小值是0，据此即可确定原式的最大值．
解： INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/1.png" \* MERGEFORMATINET ≥0，
∴当x=±2时，有最小值0，
则当x=±2，3- INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/04/29/22/b2cf9717/SYS201404292209119073715013_DA/2.png" \* MERGEFORMATINET 有最大值是3．
故答案是：3，±2．21cnjy.com
【分析】先根据x的取值范围，判断出x﹣2和3﹣x的符号，然后再将原式进行化简．
解：∵x＜2，
∴x﹣2＜0，3﹣x＞0；
∴ ( http: / / www.21cnjy.com )+|3﹣x|=﹣（x﹣2）+（3﹣x）
=﹣x+2+3﹣x=5﹣2x．
【分析】先求出长方形的面积，再根据正方形的面积公式即可求得其边长．
解：长为 ( http: / / www.21cnjy.com / )cm，宽为 ( http: / / www.21cnjy.com / )cm的矩形的面积是 ( http: / / www.21cnjy.com / )× ( http: / / www.21cnjy.com / )=16cm2，
所以正方形的面积是16cm2，所以这个正方形的边长为 ( http: / / www.21cnjy.com / )=4cm．
故答案为：4．www.21-cn-jy.com
【分析】直接相乘化简后即可得出答案
解：.
【分析】 根据同类二次根式的定义求解
解：由题意知：2+1=2+，
解得=1.
因此当=1 QUOTE http://www.21cnjy.com/ ( http: / / www.21cnjy.com ) 时两最简二次根式可以合并.
【分析】先进行二次根式的化简，然后合并即可．
解：原式=3+2 ( http: / / www.21cnjy.com )+ ( http: / / www.21cnjy.com )
= ( http: / / www.21cnjy.com )．
【分析】根据二次根式有意义的条件，得2x-1=0，x= INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/0.png" \* MERGEFORMATINET ，然后求得y的值，最后代入 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/1.png" \* MERGEFORMATINET 求解．
解：二次根式有意义，则 INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/2.png" \* MERGEFORMATINET ，
解得x= INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/e78ce56e/SYS201405131457363242473025_DA/3.png" \* MERGEFORMATINET ．
∴y==4．
∴==3．21教育网
【分析】将x、y的值化简，分别求出x+y、xy的值，根据x2+y2=（x+y）2-2xy求解．
解：∵x==-，y==+，
∴x+y=2，xy=1，
∴x2+y2=（x+y）2-2xy=（2）2-2=10．
故本题答案为10．【来源：21cnj*y.co*m】
1 、解答题
【分析】二次根式的加减，首先要把各项化为最简二次根式，是同类二次根式的才能合并，不是同类二次根式的不合并 21·世纪*教育网
解：（1） ( http: / / www.21cnjy.com / )+ ( http: / / www.21cnjy.com / )= + =-1+ 8=7
（2）;
（3） INCLUDEPICTURE "http://img./STSource/2014/06/27/18/ea7bdb3d/SYS201406271859418665271334_DA/SYS201406271859418665271334_DA.010.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/06/27/18/ea7bdb3d/SYS201406271859418665271334_DA/SYS201406271859418665271334_DA.010.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/06/27/18/ea7bdb3d/SYS201406271859418665271334_DA/SYS201406271859418665271334_DA.010.png" \* MERGEFORMATINET .
【分析】（1）分母是3 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/0.png" \* MERGEFORMATINET ，先化成最简二次根式，再分子、分母同乘以
（2）分子、分母同乘以 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/2.png" \* MERGEFORMATINET ；
（3）分子、分母同乘以 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/4.png" \* MERGEFORMATINET ；
（4）分子x-y可以分解成 INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/5.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/5.png" \* MERGEFORMATINET ；后，直接与分母约分，从而化去分母；
（5）分子、分母分别分解因式，然后约分．
解：（1） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/6.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/6.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/6.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/7.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/7.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/7.png" \* MERGEFORMATINET ；
（2） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/8.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/8.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/8.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/9.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/9.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/9.png" \* MERGEFORMATINET ；
（3） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/10.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/10.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/10.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/11.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/11.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/11.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/12.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/12.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/12.png" \* MERGEFORMATINET ；
（4） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/13.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/13.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/13.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/14.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/14.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/14.png" \* MERGEFORMATINET ；
（5） INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/15.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/15.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/15.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/16.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/16.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/16.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/17.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/17.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/14/12/98150936/SYS201405141227325104749000_DA/17.png" \* MERGEFORMATINET ．
【分析】（1）先把各二次根式化为最简二次根式，然后合并即可；
（2）先利用二次根式的除法和乘法法则运算，然后合并即可．
解：（1）原式=9 ( http: / / www.21cnjy.com )﹣14 ( http: / / www.21cnjy.com )+20 ( http: / / www.21cnjy.com )
=15 ( http: / / www.21cnjy.com )；
（2）原式= ( http: / / www.21cnjy.com )﹣ ( http: / / www.21cnjy.com )+2 ( http: / / www.21cnjy.com )
=4﹣ ( http: / / www.21cnjy.com )+2 ( http: / / www.21cnjy.com )
=4+ ( http: / / www.21cnjy.com )．
【分析】根据二次根式的被开方数是非负数即可求得a的值，进而求得b的值．
解：根据题意得： ( http: / / www.21cnjy.com )，
解得：a=5，
则b+4=0，解得：b=﹣4．
【分析】利用二次根式的性质化简即可
解：由题意得
原式=-a-1+b-1-(b-a)
=-2
【分析】可先把原式化简再代入计算，主要是根据被开方数底数的符号开平方．
解：
=
=
=
=1．【出处：21教育名师】
【分析】由三边关系定理，得到关系式；判断出被开方数的正负，再化简开方，得出结果．
解：由三边关系定理，得3+5＞c，5-3＜c，即8＞c＞2，
INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/0.png" \* MERGEFORMATINET = INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/1.png" \* MERGEFORMATINET
=c-2-（4- INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/2.png" \* MERGEFORMATINET c）=c-2-4+ INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/3.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/3.png" \* MERGEFORMATINET c= INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/4.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/13/14/5212b569/SYS201405131454209154530018_DA/4.png" \* MERGEFORMATINET c-6．【版权所有：21教育】
【分析】（1）根据正方体相对两面的代数式的值相等可列出方程组，从而解出即可得出答案．
（2）根据（1）的结果，将各组数据分别代入可判断出结果．
解：1）依题意，得 INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/0.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/0.png" \* MERGEFORMATINET ，
由 ①、②得方程组： INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/1.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/1.png" \* MERGEFORMATINET ，
解得： INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/2.png" \* MERGEFORMATINET INCLUDEPICTURE "http://img./STSource/2014/05/15/09/c1c6a28c/SYS201405150908500373488019_DA/2.png" \* MERGEFORMATINET ，
由③得：c=±2，
∴a=3，b=1，c=±2．
（2）当a=3，b=1，c=-2 时
a+b-c=3+1+2=6，
a=3，b=1，c=2时
a+b-c=3+1-2=2，
∵和都是无理数
∴a+b-c 的平方根是无理数．21*cnjy*com
( http: / / www.21cnjy.com / )
HYPERLINK "http://www.21cnjy.com/" 版权所有@21世纪教育网(www.21cnjy.com)
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