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2021年代数式知识点总结.pdf

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1、第一章有理数1、有理数(1)有理数的定义：能写成)0pq,p(pq为整数且形式的数。(2)有理数的分类：负分数负整数负有理数零正分数正整数正有理数有理数负分数正分数分数负整数零正整数整数有理数注意：0 即不是正数，也不是负数；-a不一定是负数，+a也不一定是正数；(不是有理数。2、数轴：数轴是规定了原点、正方向、单位长度的一条直线。3、相反数(1)只有符号不同的两个数；0 的相反数还是 0；(2)相反数的和为0(a+b=0(a、b 互为相反数；(3)数 a的相反数是-a，一个正数的绝对值是它本身，一个负数的绝对值是它的相反数，0 的绝对值是 0 4、绝对值(1)正数的绝对值是其本身，0 的

2、绝对值是 0，负数的绝对值是它的相反数；注意：绝对值的意义是数轴上表示某数的点离原点的距离。(2)绝对值可表示为：)0a(a)0a(0)0a(aa或)0a(a)0a(aa。5、倒数：乘积为 1 的两个数互为倒数；注意：0 没有倒数。若 a0，那么a的倒数是a1；若 ab=1(a、b 互为倒数；若 ab=-1(a、b 互为负倒数)。6、有理数比大小(1)正数的绝对值越大，这个数越大；(2)正数永远比 0 大，负数永远比0 小；(3)正数大于一切负数；(4)两个负数比大小，绝对值大的反而小；(5)数轴上的两个数，右边的数总比左边的数大。7、有理数加法法则(1)同号两数相加，取相同的符号，并把绝对值

3、相加；|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 6 页(2)异号两数相加，取绝对值较大的符号，并用较大的绝对值减去较小的绝对值；(3)一个数与 0 相加，仍得这个数。8、有理数加法的运算律(1)加法的交换律：a+b=b+a；(2)加法的结合律：(a+b)+c=a+(b+c)。9、有理数减法法则：减去一个数，等于加上这个数的相反数；即a-b=a+(-b)。10、有理数乘法法则(1)两数相乘，同号为正，异号为负，并把绝对值相乘；(2)任何数同零相乘都得零；(3)几个数相乘，有一个因式为零，积为零；各个因式都不为零，积的符号由负因式的

4、个数决定。11、有理数乘法的运算律(1)乘法的交换律：ab=ba；(2)乘法的结合律：(ab)c=a(bc)；(3)乘法的分配律：a(b+c)=ab+ac。12、有理数除法法则：除以一个数等于乘以这个数的倒数。注意：零不能做除数，即0a没意义。13、乘方的定义(1)乘方是求相同因式积的运算；(2)乘方中，相同的因式叫做底数，相同因式的个数叫做指数，乘方的结果叫做幂。14、有理数乘方的法则(1)正数的任何次幂都是正数；(2)负数的奇次幂是负数；负数的偶次幂是正数。15、混合运算法则：先乘方，后乘除，最后加减。16、科学记数法：把一个数记成a10n的形式，其中 a是整数数位只有一位的数。17、近似

5、数的精确位：一个近似数，四舍五入到那一位，就说这个近似数的精确到那一位。18、有效数字：从左边第一个不为零的数字起，到精确的位数止。|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 6 页文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3

6、HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O

7、5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3

8、HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O

9、5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3

10、HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O

11、5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3第二章整式1、单项式：在代数式中，若只含有乘法(包括乘方)运算。或虽含有除法运算，但除式中不含字母的一类代数式。2

12、、单项式的系数与次数(1)单项式的系数是单项式中不为零的数字因数；(2)单项式的次数是系数不为零时，单项式中所有字母指数的和。3、多项式：几个单项式的和叫多项式。4、多项式的项数与次数多项式中所含单项式的个数就是多项式的项数，每个单项式叫多项式的项；多项式里，次数最高项的次数叫多项式的次数。5、平方差公式：22)(bababa。6、完全平方公式：2222)(bababa。7、同底数幂的乘法法则：nmnmaaa(m，n 都是正数)。8、幂的乘方法则：mnnmaa)(m，n 都是正数)。).(),()(,为奇数时当为偶数时当一般地nanaannn9、同底数幂的除法法则：同底数幂相除，底数不变，指

13、数相减，即nmnmaaa(a0，m、n 都是正数，且 mn)；在应用时需要注意以下几点：法则使用的前提条件是同底数幂相除而且 0 不能做除数，所以法则中a0；任何不等于 0 的数的 0 次幂等于 1，即)0(10aa，则 00无意义；任何不等于 0 的数的-p 次幂(p 是正整数)，等于这个数的p 的次幂的倒数，即ppaa1(a0，p 是正整数)。10、整式的乘法(1)单项式乘法法则：单项式相乘，把它们的系数、相同字母分别相乘；(2)单项式与多项式相乘：单项式乘以多项式，是通过乘法对加法的分配律，把它转化为单项式乘以单项式，即单项式与多项式相乘，就是用单项式去乘多项式|精.|品.|可.|编.

14、|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 6 页文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F

15、3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B

16、5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F

17、3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B

18、5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F

19、3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B

20、5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3的每一项，再把所得的积相加；(3)多项式与多项式相乘：先用一个多项式中的每一项乘以另一个多项式的每一项，再把所得的积相加。11、整式的除法(1)单项式除法单项式：单项式相除，把系数、同底数幂分别相除；(2)多项式除以单项式：多项式除以单项式，先把这个多项式的每一项除以单

21、项式，再把所得的商相加。12、分解因式：把一个多项式化成几个整式的积的形式。13、分解因式的一般方法：(1)提公共因式法；(2)运用公式法；(3)十字相乘法；14、分解因式的步骤：(1)先看各项有没有公因式，若有，则先提取公因式；(2)再看能否使用公式法；(3)用分组分解法，即通过分组后提取各组公因式或运用公式法来达到分解的目的；(4)因式分解的最后结果必须是几个整式的乘积，否则不是因式分解；(5)因式分解的结果必须进行到每个因式在有理数范围内不能再分解为止。|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 6 页文档编码:CW3L6

22、P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 Z

23、N7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6

24、P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 Z

25、N7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6

26、P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 Z

27、N7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6

28、P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3第三章分式1、分式：形如 A/B，A、B 是整式，B 中含有未知数且 B 不等于 0 的整式。其中 A 叫做分式的分子，B 叫做分式的分母。2、分式有意义的条件：分母不等于 0。3、约分：把一个分式的分子和分母的公因式(不为 1 的数)约去。4、通分：异分母的分式可以化成同分母的分式。分式的基本性质：分式的分子和分母同时乘以(或除以)同一个不为 0 的整式，分式的值不变。用式子

29、表示为：A/B=A*C/B*C A/B=A C/B C(A，B，C 为整式，且 C 0)5、最简分式：一个分式的分子和分母没有公因式。约分时，一般将一个分式化为最简分式。6、分式的加减法则(1)同分母分式加减法则：同分母的分式相加减，分母不变，把分子相加减。用字母表示为：a/c b/c=a b/c；(2)异分母分式加减法则：异分母的分式相加减，先通分，化为同分母的分式，然后再按同分母分式的加减法法则进行计算。用字母表示为：a/b c/d=ad cb/bd；7、分式的乘法法则：两个分式相乘，把分子相乘的积作为积的分子，把分母相乘的积作为积的分母。用字母表示为：a/b*c/d=ac/bd。8、分式

30、的除法法则：(1)两个分式相除，把除式的分子和分母颠倒位置后再与被除式相乘。用字母表示为：a/b c/d=ad/bc；(2)除以一个分式，等于乘以这个分式的倒数：a/b c/d=a/b*d/c。|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 5 页，共 6 页文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8

31、Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:C

32、W3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8

33、Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:C

34、W3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8

35、Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:C

36、W3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3第四章根式1、平方根：一般地，如果一个数x 的平方等

37、于 a，即 x2=a，那么数 x 就叫做 a的平方根。从定义可知，只有当a0 时，a才有平方根。注意：正数有两个平方根(一正一负)它们互为相反数；0 只有一个平方根，就是它本身；负数没有平方根。2、算术平方根：一般地，如果一个正数 x 的平方等于 a，即 x2=a，那么正数 x叫做 a的算术平方根，记作a。3、立方根：一般地，如果一个数x 的立方等于 a，即 x3=a，那么数 x 就叫做 a的立方根。注意：正数的立方根是正数；0 的立方根是 0；负数的立方根是负数。4、二次根式：式子a(a0)叫做二次根式。5、最简二次根式(1)被开方数中不含开方开的尽的因数或因式；(2)被开方数中不含分母；(

38、3)分母中不含根式。6、同类二次根式二次根式化成最简二次根式后，若被开方数相同，则这几个二次根式就是同类二次根式。7、二次根式的性质(1)(a)2=a(a0)；(2)aa28、二次根式的运算(1)因式的外移和内移：如果被开方数中有的因式能够开得尽方，那么，就可以用它的算术根代替而移到根号外面；如果被开方数是代数和的形式，那么先解因式，?变形为积的形式，再移因式到根号外面，反之也可以将根号外面的正因式平方后移到根号里面；(2)二次根式的加减法：先把二次根式化成最简二次根式再合并同类二次根式；(3)二次根式的乘除法：二次根式相乘(除)，将被开方数相乘(除)，所得的积(商)仍作积(商)的被开方数并将

39、运算结果化为最简二次根式：ab=ab(a0，b0)；bbaa(b0，a0)。a(a0)a(a0)0(a=0)；|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 6 页，共 6 页文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4

40、 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3

41、L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4

42、 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3

43、L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4

44、 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3文档编码:CW3L6P6T3F3 HZ7P5L9P8Z4 ZN7Y3B5O5D3

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