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【330032】16.1 二次根式(2)

时间:2025-02-07 09:18:57 作者: 字数:2729字

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

161 二次根式(2)学案

课型: 上课时间: 课时:

学习内容:

1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数; 2.( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=aa≥0).

学习目标:

1、理解 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数和( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=aa≥0),并利用它进行计算和化简.

2、通过复习二次根式的概念,用逻辑推理的方法推出 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数,用具体数据结合算术平方根的意义导出( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=aa≥0);最后运用结论严谨解题.

教学过程

一、自主学习

(一)复习引入

1.什么叫二次根式?

2.当a≥0时, <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 叫什么?当a<0时, <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义吗?

(二)学生学习课本知识

(三)、探究新知

1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个 数。(正数、负数、零)

因为

2重点: <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数.

3、根据算术平方根的意义填空:

 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=_______;( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=_______;( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=______;( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=_______

同理可得:( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=2, ( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=9, ( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=3, ( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2= <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , ( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=0

所以  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=aa≥0

(4) 1 计算

1、( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 = 2、(3 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 = 3、( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 = 4、( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=

(5)注意:1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数;( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=aa≥0)及其运用.

2、用分类思想的方法导出 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数;用探究的方法导出( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=aa≥0).

二、学生小组交流解疑,教师点拨、拓展

2 计算 1.( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2x≥02.( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 3.( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

3 在实数范围内分解下列因式:

1x2-3 2x4-4 (3) 2x2-3

三、巩固练习

(一)计算下列各式的值:

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

(二) 课本P71

四、课堂检测

(一)、选择题

1.下列各式中 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,二次根式的个数是( ).

A4 B3 C2 D1

(二)、填空题

1.(- <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=________2.已知 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义,那么是一个_______数.

(三)、综合提高题

1.计算

1)( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 2-- <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 3)(-3 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 (4)  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= = = =

= = = =

2.把下列非负数写成一个数的平方的形式:

15= 23.4= 3 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4xx≥0=

3.已知 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =0,求xy的值.

4.在实数范围内分解下列因式:

1x2-2 2x4-9 3x2-5