What is the greatest perfect square possible?

Answer 1

There is no limit to the number of perfect squares. To find a perfect square, you simply need to pick a number and square it. E.g. 7^2=49, so 49 is a perfect square.

As there is infinitely many numbers to pick, and as the larger a number the larger it's square, there are infinitely many perfect squares and they just keep on getting larger!