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【329732】5.2二次根式的乘法和除法(1)

时间:2025-02-03 19:06:27 作者: 字数:2215字

5.2二次根式的乘法和除法(一)导学案

【学习目标】

  1. 掌握二次根式的乘法法则: <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. 熟练进行二次根式的乘法运算及化简。

【学习重点】理解并掌握二次根式的乘法法则。

【学习难点】理解并掌握二次根式的乘法法则。

【学习过程】

一、学前准备

说一说:积的算术平方根的性质是什么?

 <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>

把这个公式从右到左写写看:_____________= <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> ,能当公式用吗?

二、探索思考

阅读课本P161——162


知识点一 : 二次根式的乘法

学一学:阅读教材例1、例2,你还有问题吗?计算:相信你行。

⑴  <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> ⑶  <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>






议一议:1.乘法运算律和乘法公式在二次根式运算中仍然适用吗?

2.二次根式的运算结果要注意什么?




【归纳总结】1.二次根式的乘法法则是: <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> ,语言叙述为两个二次根式相乘,把_____________相乘,根指数不变。

2.二次根式的运算结果一定要化简,化简时,通常是先把根号下的每个数分解因数,然后把每一个_______________去掉平方号后移到____________外。

3.乘法运算律和乘法公式在二次根式运算中仍然___________




【课堂展示】1.下列计算错误的是( )


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>

  1. 计算下列各题,其中 <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>

⑴  <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> ⑶ <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> 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>









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> 计算:

⑴  <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> ⑶  <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>










4.已知矩形的一边长 <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> ㎝,邻边长 <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> ㎝,求矩形的面积和对角线的长。









5.计算⑴  <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> ⑶  <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. 当堂反馈

  1. ⑴  <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> ⑶  <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>







2.P162练习








课堂小结 本节课你学到了那些知识?








、学习反思