Supposed you list the factors of a perfect square why is one factor a square root and not the other factors ?

No factor of a perfect square is a square root, (unless it's the square root of a perfect-
square number, and then it can be replaced by the number that's the square root of
what's inside the radical).

The  factors of a perfect square are just whole numbers.

256 is a perfect square.

Its factors are 1, 2, 4, 8, 16, 32, 64, 128, and 256.