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,
`(x^2)(y^2)`
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 xx (31)^2 = 729 xx 961 = 700,569`

`sqrt700569 = 837`