Question

Is the product of two perfect squares always a perfect square?

Answer 1

Yes!
Explanation:
Suppose that one of the squares is $x^2$ and the other is $y^2$.
Their product,
$\left(x^2\right)\left(y^2\right)$
will be equal to $(xy{)}^2$, which is also a perfect square.
By the same reason, the product of any number of perfect squares is a perfect square.
Let's take an example to confirm this.
$(27{)}^2\times (31{)}^2=729\times 961=700,569$
$\sqrt{700569}=837$