Find the biggest 4-digit number that is a perfect square.

A perfect square is a number of the form n2 for some integer n. To find the largest k-digit perfect square, find the largest integer n such that n2 still has exactly k digits — this n is the integer part of the square root of the largest k-digit number.

1. The largest 4-digit number is 9999.

2. Its square root, √9999, is approximately 99.995.

3. The greatest integer not exceeding 99.995 is 99, so n = 99.

4. Square 99: 992 = 9801, a 4-digit number.

Cross-check: the next integer, 100, gives 1002 = 10000, which already has 5 digits. So 992 = 9801 is confirmed as the largest 4-digit perfect square.