Question

Find the greatest 4-digit number which is a perfect square.

Answer 1

Greatest number of 4-digits = 9999.

We find `sqrt(9999)` by long division method. The remainder is 198.

This shows 99² is less than 9999 by 198.

This means if we subtract the remainder from the number, we get a perfect square.

Therefore, the required perfect square is 9999 - 198 = 9801.

And, `sqrt(9801) = 99.`