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【329890】9.3 二次根式的乘法与除法(1)

时间:2025-02-07 09:22:50 作者: 字数:1696字



9.3 二次根式的乘法与除法(1


【学习目标】

了解二次根式的乘除法的法则,会运用法则进行二次根式简单的乘除运算.

【知识准备】

 <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,b≥0)    <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,b0

【自学提示】

把上面积的算术平方根与商的算术平方根的性质逆向使用,你能得到两个等式?把它们写出


____________________________________________________________________________.

我们把上面的两个等式分别作为二次根式的乘法和除法法则.

【问题积累】

你还有哪些不明白的问题?

【共同释疑】

1 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>                   ⑵ <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>                      ⑷ <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>



与同桌对照,⑷的解法有没有不同?



对应练习

1、计算:

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>



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>

2、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>                   ⑵ <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>





3、挑战自我

 <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> 哪个大?你是怎样比较它们的大小的?




小结:二次根式的乘法和除法法则:


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【当堂测试】

1、下列各等式成立的是( ).

A4 <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> =8 <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> B5 <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> =20 <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>

C4 <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> =7 <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> D5 <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> =20 <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、计算:

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> · <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> · <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>




3、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>            ⑵ <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>