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

Dec 4, 2016

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 ${\left(x y\right)}^{2}$, 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.

${\left(27\right)}^{2} \times {\left(31\right)}^{2} = 729 \times 961 = 700 , 569$

$\sqrt{700569} = 837$