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Problem 80

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Square root digital expansion

It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all.

The square root of two is $1.41421356237309504880\ldots$, and the digital sum of the first one hundred decimal digits is $475$.

For the first one hundred natural numbers, find the total of the digital sums of the first one hundred decimal digits for all the irrational square roots.

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平方根数字展开

众所周知，如果一个自然数的算术平方根不是整数，那么就一定是无理数，也即无限不循环小数。

$2$的算术平方根为$1.41421356237309504880\ldots$，它的前一百个数字（包括小数点前的$1$）的和是$475$。

考虑前一百个自然数的算术平方根，求其中所有无理数的前一百个数字的总和。

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