步骤/方法
小于 30的自然数，二次方顶多只有三位数，其他数字计算二次方，就要用它们作 b" ，我们就要先熟悉它们。它们自己计算二次方，只要用 1到5 作 b，把 (a+b)或(a-b)变成整十，轻松相乘算出平方差，再把 b" 加回去。
两位数 25 到 50，b 就利用 1 到 25，把 (a+b) 变成 50。(a-b)就是 [(a+b)-2b]，这个 2b 肯定是偶数，(a+b)=50 也是偶数，那么(a-b) =[(a+b)-2b] 还是偶数，相乘得到的平方差就又是整百，这样再把 b" 加回去，整百与三位数相加也同样方便。
两位数 50 到 75，b 就利用 1 到 25，把 (a-b) 变成 50 来计算。(a+b)与(a-b) 相乘得到的平方差就还是整百，这样再把 b" 加回去，整百与三位数相加也同样方便。
两位数 75 到三位数 125，不用说相信大家也知道，b 利用 1 到 25，把 (a+b)或者(a-b) 变成 100 来计算，情况就与 25到75 的两位数差不多，算起来甚至感觉更简便。
500 前面的三位数，计算二次方，我们就根据最后的两位数，还是像这样计算。
连续的二次方算一算
方法分析到这里，我们来算一算 25 到 125 的二次方吧。好方法可要用一用才有感受啊！
25" = 20 X 30 + 25 = 625 26" = (26-24)(26+24) + 24" = 2 X 50 + 576 = 100 + 576 = 676 27" = (27-23)(27+23) + 23" = 4 X 50 + 529 = 200 + 529 = 729 28" = (28-22)(28+22) + 22" = 6 X 50 + 484 = 300 + 484 = 784 29" = (29-21)(29+21) + 21" = 8 X 50 + 441 = 400 + 441 = 841
30" = 30 X 30 = 900 31" = (31-19)(31+19) + 19" = 12 X 50 + 361 = 600 + 361 = 961 32" = (32-18)(32+18) + 18" = 14 X 50 + 324 = 700 + 324 = 1024 33" = (33-17)(33+17) + 17" = 16 X 50 + 289 = 800 + 289 = 1089 34" = (34-16)(34+16) + 16" = 18 X 50 + 256 = 900 + 256 = 1156
35" = 30 X 40 + 25 = 1225 36" = (36-14)(36+14) + 14" = 22 X 50 + 196 = 1100 + 196 = 1296 37" = (37-13)(37+13) + 13" = 24 X 50 + 169 = 1200 + 169 = 1369 38" = (38-12)(38+12) + 12" = 26 X 50 + 144 = 1300 + 144 = 1444 39" = (39-11)(39+11) + 11" = 28 X 50 + 121 = 1400 + 121 = 1521
40" = 40 X 40 = 1600 41" = (41-9)(41+9) + 9" = 32 X 50 + 81 = 1600 + 81 = 1681 42" = (42-8)(42+8) + 8" = 34 X 50 + 64 = 1700 + 64 = 1764 43" = (43-7)(43+7) + 7" = 36 X 50 + 49 = 1800 + 49 = 1849 44" = (44-6)(44+6) + 6" = 38 X 50 + 36 = 1900 + 36 = 1936
45" = 40 X 50 + 25 = 2025 46" = (46-4)(46+4) + 4" = 42 X 50 +16 = 2100 +16 = 2116 47" = (47-3)(47+3) + 3" = 44 X 50 + 9 = 2200 + 9 = 2209 48" = (48-2)(48+2) + 2" = 46 X 50 + 4 = 2300 + 4 = 2304 49" = (49-1)(49+1) + 1" = 48 X 50 + 1 = 2400 + 1 = 2401
50" = 50 X 50 = 2500 两位数 25到50 的二次方，我们全都算过了，(a+b)变成50，b 从1到25，我们都用过一遍了，后面其余数字的计算，(a-b)(a+b) 这一步我就省略不写了。 51" = 52 X 50 + 1" = 2600 + 1 = 2601 52" = 54 X 50 + 2" = 2700 + 4 = 2704 53" = 56 X 50 + 3" = 2800 + 9 = 2809 54" = 58 X 50 + 4" = 2900 +16 = 2916
55" = 60 X 50 + 25 = 3025 56" = 62 X 50 + 6" = 3100 + 36 = 3136 57" = 64 X 50 + 7" = 3200 + 49 = 3249 58" = 66 X 50 + 8" = 3300 + 64 = 3364 59" = 68 X 50 + 9" = 3400 + 81 = 3481
60" = 60 X 60 = 3600 61" = 72 X 50 + 11" = 3600 + 121 = 3721 62" = 74 X 50 + 12" = 3700 + 144 = 3844 63" = 76 X 50 + 13" = 3800 + 169 = 3969 64" = 78 X 50 + 14" = 3900 + 196 = 4096
65" = 60 X 70 + 25 = 4225 66" = 82 X 50 + 16" = 4100 + 256 = 4356 67" = 84 X 50 + 17" = 4200 + 289 = 4489 68" = 86 X 50 + 18" = 4300 + 324 = 4624 69" = 88 X 50 + 19" = 4400 + 361 = 4761
70" = 70 X 70 = 4900 71" = 92 X 50 + 21" = 4600 + 441 = 5041 72" = 94 X 50 + 22" = 4700 + 484 = 5184 73" = 96 X 50 + 23" = 4800 + 529 = 5329 74" = 98 X 50 + 24" = 4900 + 576 = 5476
75" = 70 X 80 + 25 = 5625 两位数 50到75 的二次方，我们也都算过了，(a-b)变成50，b 从1到25，我们又用过了一遍 76" = 52 X 100 + 24" = 5200 + 576 = 5776 77" = 54 X 100 + 23" = 5400 + 529 = 5929 78" = 56 X 100 + 24" = 5600 + 484 = 6084 79" = 58 X 100 + 21" = 5800 + 441 = 6241
80" = 80 X 80 = 6400 81" = 62 X 100 + 19" = 6200 + 361 = 6561 82" = 64 X 100 + 18" = 6400 + 324 = 6724 83" = 66 X 100 + 17" = 6600 + 289 = 6889 84" = 68 X 100 + 16" = 6800 + 256 = 7056
85" = 80 X 90 + 25 = 7225 86" = 72 X 100 + 14" = 7200 + 196 = 7396 87" = 74 X 100 + 13" = 7400 + 169 = 7569 88" = 76 X 100 + 12" = 7600 + 144 = 7744 89" = 78 X 100 + 11" = 7800 + 121 = 7921
90" = 90 X 90 = 8100 91" = 82 X 100 + 9" = 8200 + 81 = 8281 92" = 84 X 100 + 8" = 8400 + 64 = 8464 93" = 86 X 100 + 7" = 8600 + 49 = 8649 94" = 88 X 100 + 6" = 8800 + 36 = 8836
95" = 90 X 100 + 25 = 9025 96" = 92 X 100 + 4" = 9200 +16 = 9216 97" = 94 X 100 + 3" = 9400 + 9 = 9409 98" = 96 X 100 + 2" = 9600 + 4 = 9604 99" = 98 X 100 + 1" = 9800 + 1 = 9801
100" = 100 X 100 = 10000 前面的 75到100 算平方，就要用 b 从 1到25，把 (a+b)变成100， 接下来 100到125 算平方，又是用 b 从 1到25，把 (a-b)变成100 来计算。 101" = 102 X 100 + 1" = 10200 + 1 = 10201 102" = 104 X 100 + 2" = 10400 + 4 = 10404 103" = 106 X 100 + 3" = 10600 + 9 = 10609 104" = 108 X 100 + 4" = 10800 + 16 = 10816
105" = 110 X 100 + 5" = 11000 + 25 = 11025 106" = 112 X 100 + 6" = 11200 + 36 = 11236 107" = 114 X 100 + 7" = 11400 + 49 = 11449 108" = 116 X 100 + 8" = 11600 + 64 = 11664 109" = 118 X 100 + 9" = 11800 + 81 = 11881
110" = 110 X 110 = 12100 111" = 122 X 100 + 11" = 12200 + 121 = 12321 112" = 124 X 100 + 12" = 12400 + 144 = 12544 113" = 126 X 100 + 13" = 12600 + 169 = 12769 114" = 128 X 100 + 14" = 12800 + 196 = 12996
115" = 130 X 100 + 15" = 13000 + 225 = 13225 116" = 132 X 100 + 16" = 13200 + 256 = 13456 117" = 134 X 100 + 17" = 13400 + 289 = 13689 118" = 136 X 100 + 18" = 13600 + 324 = 13924 119" = 138 X 100 + 19" = 13800 + 361 = 14161
120" = 120 X 120 = 14400 121" = 142 X 100 + 21" = 14200 + 441 = 14641 122" = 144 X 100 + 22" = 14400 + 484 = 14884 123" = 146 X 100 + 23" = 14600 + 529 = 15129 124" = 148 X 100 + 24" = 14800 + 576 = 15376
125" = 150 X 100 + 25" = 15000 + 625 = 15625 数字这样计算二次方，感觉是不是方便多了呢？
正如平方数的末位数就只有 0、1、4、9、6、5 这6个，平方数的最后两位，也只有 1到25 这二十几个，有趣吧。 十位数是 0、4、5、9，二次方的后两位，也就是 1到9 的平方值 十位数是 1、3、6、8，二次方的后两位就都是 21、44、69、96、25、56、89、24、61 十位数是 2、7，二次方的后两位也都是 41、84、29、76、25