平方:
11 ^2 = 121
12 ^2 = 144
13 ^2 = 169
14 ^2 = 196
15 ^2 = 225
16 ^2 = 256
17 ^2 = 289
18 ^2 = 324
19 ^2 = 361
20 ^2 = 400
21 ^2 = 441
10以内的平方数,应该不用列出来了,各位都知道。
相邻平方数之间是有规律的,所以也不用全记住
a^2 – b^2 = (a b)(a-b)
因为相邻,a-b=1,
So,a^2 = b^2 b a,
例:14^2 = 13^2 13 14
=169 1 12 14
=170 26
=196
立方:
2 ^3 = 8
3 ^3 = 27
4 ^3 = 64
5 ^3 = 125
6 ^3 = 216
7 ^3 = 343
8 ^3 = 512
9 ^3 = 729
10 ^3 = 1000
11 ^3 = 1331
12 ^3 = 1728
13 ^3 = 2197
14 ^3 = 2744
15 ^3 = 3375
16 ^3 = 4096
17 ^3 = 4913
18 ^3 = 5832
19 ^3 = 6859
20 ^3 = 8000
21 ^3 = 9261
10以内的立方数,还是要死记硬背下,10以上的嘛,还是尽量记,实在想不起可以借助公式
(a b)^3 = a^3 3a^2b 3ab^3 b^3
也就是说把 十几 拆开来
例 17^3 = (10 7)^3
= 10^3 3*10^2*7 3*10*7^2 7^3
=1000 2100 30*49 343
=3100 30*(50-1) 343
= 3100 1500 313
=4913
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