当前位置:首页 > 八年级 > 数学试卷

【329734】5.2二次根式的乘法和除法

时间:2025-02-03 19:06:39 作者: 字数:7669字



5.2二次根式的乘法和除法同步测试

一、选择题

1.下列二次根式中,最简二次根式的是(   )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                       B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                     

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                     D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2.下列式子为最简二次根式的是(     )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                        B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                    

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                     D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3.下列式子中,属于最简二次根式的是(  )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                     B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                     

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                       D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

4.下列二次根式中,与 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 之积为无理数的是(  )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                        B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                      

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                        D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

5.下列根式是最简二次根式的是(   )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                        B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                      

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                         D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

6.下列各式是最简二次根式的是(   )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                        B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                    

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                       D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

7.在根式①  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 中,最简二次根式是(   )

A. ①②                       B. ③④                                     

C. ①③                       D. ①④

8.下列式子中,属于最简二次根式的是(   )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                         B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                       

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                        D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


9.下列二次根式中,属于最简二次根式的是(   )

A.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                          B.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                       

C.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                           D.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

10.计算: <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是(  )

A. 9 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                          B. 3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                                      

C. 2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>                          D. 3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

二、填空题

11.计算  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是________

12.化简  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果为________

13.计算 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =________

14.若一个长方体的长为  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm,宽为  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm,高为  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm,则它的体积为________cm3

15.计算  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0=________

16. <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ×(﹣  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =________

17.化简: <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =________ 

18.计算: <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =________ 

三、解答题

19.把下列二次根式化成最简二次根式.
1 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>










  1. 已知:实数ab在数轴上的位置如图所示,化简: <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> |a﹣b|
     <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>











  1. 把下列二次根式化成最简二次根式.
    1 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
    2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
    3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
    4 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>










22.化简:4x2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


参考答案

一、选择题

1.C

2.C

3.C

4.B

5.C

6.B

7.C

8.B

9.D

10.B

二、填空题

11.2

12. <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

13. <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

14.12

15.4a

16.﹣3  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

17.  <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

18. <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

三、解答题

19.解:(1 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

20.解:从数轴上ab的位置关系可知:﹣2a<﹣11b2,且ba
a+10b﹣10a﹣b0
原式=|a+1|+2|b﹣1|﹣|a﹣b|
=﹣a+1+2b﹣1+a﹣b
=b﹣3

21.解:(1 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
4 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

22.解:4x2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
=4x2÷12×3 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
=x2 <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
=xy