Q: What is the sum of the digits of the square of ?

A: 81

Using the standard multiplication algorithm, whose digit sum is 81.

Or by looking at the pattern:

whose digit sum is 81

There is a shortcut to adding these digits

Reading from left to right, we can add the first 8 digits, 1 through 8 by making 4 pairs of 9 (1 + 8, 2 + 7, 3 + 6 and 4 + 5) making 36

Reading from right to left, we can add the last 8 digits (1- 8) the same way making 36.

Leaving the middle digit of 9.

36 + 36 + 9 = 81