∵1<2<4
∴√1<√2<√4
即1<√2<2
∴根号2的小数部分=√2-1
(√2-1)²=2+1-2√2=3-2√2
[根号1]+[根号2]+[根号3]+...+[根号100]
=1+1+1+2+2+2+2+2+3×7+4×9+5×11+6×13+7×15+8×17+9×19+10
=625
∵1<2<4
∴√1<√2<√4
即1<√2<2
∴根号2的小数部分=√2-1
(√2-1)²=2+1-2√2=3-2√2
[根号1]+[根号2]+[根号3]+...+[根号100]
=1+1+1+2+2+2+2+2+3×7+4×9+5×11+6×13+7×15+8×17+9×19+10
=625