I did it by trial and error.
7^2 is 49.
4 + 9 = 13
81
Every square of a 4 digit number has more than four digits.
81...........
81
121
81
49
Every square of a 4 digit number has more than four digits.
81...........
81
1
121
81
algorithm is a way to solve your problem
The largest 3-digit number - not itself a perfect square - is 999. Calculate its square root, round the answer down, then square the answer again.
The number is 81.
The square root of 55 is an irrational number, meaning it never ends and doesn't have a repeating digit pattern, so it has an infinite number of digits.