Find the greatest four-digit number that is a perfect square.

The largest four-digit number is 9999.

We need the greatest perfect square less than or equal to 9999.

$100^2 = 10000 \quad (\text{5-digit number})$

So, the next lower square is:

$99^2 = 9801$

Therefore, the greatest four-digit perfect square is: 9801​