math question

The perfect squares:  1, 4, 9, 16, 25, 36, ...

are closed with respect to multiplication

because:

Since each member of the set of perfect squares has a square root that is a whole number, 

let the set of square roots be:  1, a, b, c, d, ...

then the set of perfect squares is:  1, a², b², c², d², ...

Choose any two members of the set of perfect squares, say  x²  and  y²,

then  x²·y²  =  (xy)²,  which is a perfect square.