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their nervous systems and ability to produce baby birds, and can lead to kidney(肾) failures and death. So condors with high levels of lead are sent to Los Angeles Zoo, where they are treated with calcium EDTA, a chemical that removes lead from the blood over several days. This work is starting to pay off. The annual death rate for adult condors has dropped from 38% in 2000 to 5.4% in 2011. 16.1.1二次根式的概念

导学案

学习目标

1．掌握二次根式的概念，并利用a（a≥0）的意义解答具体题目. 2. 提出问题，根据问题给出概念，应用概念解决实际问题. 重点：熟知并正确的理解二次根式的概念. 难点：利用a（a≥0）的意义解答具体题目. 一、自学释疑

二次根式应满足哪两个条件？

二、合作探究

探究点一、二次根式的概念及有无意义，被开方数中未知数的取值范围问题. 问题1.下列式子，哪些是二次根式，哪些不是二次根式：

112、33、、x（x>0）、0、42、-2、、x?y（x≥0，y??≥0）．

x?yx解：二次根式有：；不是二次根式的有：。

问题2．在式子解：由得：。

1?2x1?x中，x的取值范围是____________.

注意：1、形如a（a≥0）的式子是二次根式的概念；即含有根号，根指数要为2.

their nervous systems and ability to produce baby birds, and can lead to kidney(肾) failures and death. So condors with high levels of lead are sent to Los Angeles Zoo, where they are treated with calcium EDTA, a chemical that removes lead from the blood over several days. This work is starting to pay off. The annual death rate for adult condors has dropped from 38% in 2000 to 5.4% in 2011. 2、利用“a?0，且（a≥0）”解决具体问题

3、结论：要使二次根式在实数范围内有意义，必须满足被开方数是非负数。 强化训练

1.试一试：判断下列各式，哪些是二次根式？哪些不是？为什么？

3，?16，34，?5，a(a?0)，x2?13

2.x取何值时，下列各二次根式有意义？ ①3x?4②2?23x③?12?x

探究点二、小组活动、讨论、典型例题 1.已知y=2?x+x?2+5，求

xy的值 2.若a?1+b?1=0，求a2014+b2104

的值.

强化训练2

1.若a?3?3?a有意义，则a的值为___________． 2.已知x2?4+

2x?y＝0，则x?y?_____________.

3.某工厂要制作一批体积为1m3

的产品包装盒，其高为0.2m，按设计需要，正方形，试问底面边长应是多少？

三、随堂检测

1. 下列各式中，一定是二次根式的是（ ）

底面应做成?their nervous systems and ability to produce baby birds, and can lead to kidney(肾) failures and death. So condors with high levels of lead are sent to Los Angeles Zoo, where they are treated with calcium EDTA, a chemical that removes lead from the blood over several days. This work is starting to pay off. The annual death rate for adult condors has dropped from 38% in 2000 to 5.4% in 2011. A. B.

C.

D.

2.若式子A.

在实数范围内有意义，则的取值范围是（ ）

B.≥1 C.

≥

D.

x＋1

3.要使式子x有意义，x的取值范围是( )．

A. x≠1 B. x≠0 C. x＞－1且x≠0 D. x≥－1且x≠0 4．要使A．

有意义，则x应满足（ ）．

C．

＜x＜3 D．

＜x≤3

≤x≤3 B．x≤3且x≠

，则

5.已知A.

的值为（ ）

B.

1 C. D.

6.当 时，二次根式7.小红说：“因为 8.当 我的收获

时，二次根式

，所以

无意义．

不是二次根式.”你认为小红的说法对吗？

有最小值，其最小值是 ．

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参考答案

随堂检测 1.C． 2.D． 3.D.