1.2 二次根式的性质第2课时教学课件 2025-2026学年浙教版数学八年级下册

第1章　二次根式 1.2 二次根式的性质 　第2课时　二次根式的性质 初中数学浙教版（2024）八年级下册 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 1.了解二次根式的积和商的性质，能够运用二次根式的性质将简单二次 根式化简. 2.经历二次根式性质的发现过程，体验归纳、类比的思想方法. 学习目标 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 2 二次根式有什么性质？ 计算：  ． -2a 知识回顾 性质1： =a（a≥0） 性质2： == Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 3 填空(可用计算器计算): =　　　　， ×=　　　　； =　　　　， ×=　　　　； =　　 　　， =　　 　　； =　　 　　， =　　 　　； 6 6 4.472… 议一议：比较左右两边的等式，你发现了什么?你能用字母表示发现的规 律吗? 4.472… 0.75 0.75 1.224… 1.224… 新知探究 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 4 一般地，二次根式有下面的性质: = (a≥0，b≥0) = (a≥0，b>0) 思考：你能证明二次根式积和商的性质吗？ 新知探究 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 5 =(a≥0，b≥0) 证明：∵()2= ( )2 ()2 =ab, 又∵ 0，0， ∴是ab的算术平方根， 即=(a≥0，b≥0). =(a≥0，b>0) 证明：∵()2= =, 又∵ 0，0， ∴是的算术平方根， 即=(a≥0，b>0). 新知探究 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 6 解：（1）= × =11×15=165. （2）= × =4 . （3）= = . （4）= =. 例1 化简： （1）（2）. （3）. （4）. 例题精讲 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 像, 这样，在根号内不含分母，不含开得尽方的因 数或因式，这样的二次根式我们就说它是最简二次根式. 二次根式化简的 结果应为最简二次根式. 化成最简二次根式的方法： 1.将被开方数中能开得尽方的因数或因式进行开方. 2.化去根号下的分母：被开方数是带分数的，要先化成假分数；被开方数 是小数的，要先化成假分数. 3.被开方数是多项式时要先进行因式分解. 新知探究 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 解：（1） 例2 化简: （1）. （2） . （3）. = = = × =12. 例题精讲 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 解：（2） = = = . 例2 化简: （1）. （2） . （3）. 例题精讲 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 解：（3） = = . 例2 化简: （1）. （2） . （3）. 例题精讲 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 1. 化简的结果是(　　) A.2 B.3 C.2 D.3 B 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 2.若=·，则x的取值范围是(　　) A.x≥2 B.x≤1 C.1≤x≤2 D.x≥0 A 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 13 3. 下列化简错误的是 (　　) A.== B.=×=0.1×0.7=0.07 C.== D.=×=1×= D 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 4.下列二次根式中，是最简二次根式的是(　　) A. B. C. D. B 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 5.已知 ，则 的取值范围是（ ） A. B. C. D. C 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 6.化简 的结果是（ ） A. B. C. D. B 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 17 7.化简：  ，  ． 8.若=a,则用含a的代数式表示为　　　　.  9.能使等式 成立的 的取值范围是  ． 36 100a a≥0 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 18 10.计算： (1); (2); (3); (4). 解：(1)=×=12×4=48. (2)=×=15. (3)==×=15. (4)=××=2××13=. 随堂练习 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 二次根式 的性质 1.将被开方数中能开得尽方的因数或因式 进行开方. 2.化去根号下的分母：被开方数是带分数 的，要先化成假分数；被开方数是小数的， 要先化成假分数. 3.被开方数是多项式时要先进行因式分解. 课堂小结 积和商的性质 化成最简 二次根式 的方法 积的性质： =(a≥0，b≥0) 商的性质： =(a≥0，b>0) Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS 谢谢 Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS Click to add title Click to add text Second level Third level Fourth level Fifth level OfficePLUS $