√12345678987654321=?
12345678987654321=
108+111×107+11111×106+1111111×105+111111111×104+11111111111×103+1111111111111×102+111111111111111×10+11111111111111111=
19[(10−1)×108+(103−1)×107+(105−1)×106+(107−1)×105+(109−1)×104+(1011−1)×103
+(1013−1)×102+(1015−1)×10+(1017−1)]=
19[109(1+10+102+.....+107+108)−(108+107+106+....+10+1)]=
19[(109−1)(1+10+102+.....+107+108)]=
19[(109−1)1−1091−10]=(109−19)2=1111111112
所以√12345678987654321=111111111
111111111×111111111=111111111×(1+10+102+103+.....+108)
直式算式如下
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