What is the largest 3-digit number that is a perfect square?

The largest 3-digit number is 999.

We need to find the largest integer whose square is less than or equal to 999.
Calculate the square root of 999:

Since $\sqrt{999} \approx 31.607$, the largest integer whose square is less than or equal to 999 is 31.

This is a 3-digit number.

Since 1024 is a 4-digit number, 961 is the largest 3-digit perfect square.

The largest number of 3 digits which is a perfect square is $\boxed{\text{961}}$.