is there a square, when multiplied by 3, is still a square?

3x = y

where 'x' and 'y' are both squares

I don't think so, sorry!

If your numbers are all integers then the answer is no, because sqrt(3) is irrational. If they can be reals, then yes: (sqrt(3)*a)^{2} = b^{2}, for which there are an infinite number of solutions.