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【330037】16.2 二次根式的乘除(1)

时间:2025-02-07 09:19:21 作者: 字数:2405字

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

162 二次根式的乘除(1

课型: 上课时间: 课时:

学习内容

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0),反之 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0)及其运用.

学习目标

理解 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0), <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0),并利用它们进行计算和化简

学习过程:

一、自主学习

(一)复习引入

1.填空:(1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =____ <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =____  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> __ <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =____ <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> __ <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___ <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> __ <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (二)、探索新知

1、 学生交流活动总结规律.

2、一般地,对二次根式的乘法规定为

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .(a≥0b≥0 反过来:  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0

1.计算

1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 33 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ×2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>




2 化简

1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>





二、巩固练习

1)计算: ①  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ②3 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ×2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(2) 化简:  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>



3)教材练习

三、学生小组交流解疑,教师点拨、拓展

(一)例3判断下列各式是否正确,不正确的请予以改正:

1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =4× <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =4 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =4 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =8 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(二)归纳小结

1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =a≥0b≥0), <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0)及其运用.

2)要理解 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a<0,b<0= <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,如 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

四、课堂检测

(一)、选择题

1.若直角三角形两条直角边的边长分别为 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm,那么此直角三角形斜边长是( ). A3 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm B3 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm C9cm D27cm

2.化简a <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是( ). A <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3.等式 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 成立的条件是( )

Ax≥1 Bx≥-1 C-1≤x≤1 Dx≥1x≤-1

( )填空题 1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_______

2.自由落体的公式为S= <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> gt2g为重力加速度,它的值为10m/s2),若物体下落的高度为720m,则下落的时间是_________

三、综合提高题

1.一个底面为30cm×30cm长方体玻璃容器中装满水,现将一部分水例入一个底面为正方形、高为10cm铁桶中,当铁桶装满水时,容器中的水面下降了20cm,铁桶的底面边长是多少厘米?