Question

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

Answer 1

The Greatest Perfect square of a $4$-digit number

1. An integer that can be expressed as the square of another integer is called a perfect square.
2. Square of $100$ is $10000$ which is the first $5$ digit number, so the required number must be less than $10000$ which means the square root must be less than$100$.

So, the next number must be$99$, and the square of $99$ is$9801$.

Hence the largest $4$-digit number which is a perfect square is$9801$.