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

1 Answer

Dec 4, 2016

Yes

Explanation:

Suppose that one of the squares is $x^{2}$ $x^2$ and the other is $y^{2}$ $y^2$ .

Their product,
$(x^{2}) (y^{2})$ $(x^2)(y^2)$
will be equal to ${(x y)}^{2}$ $(xy)^2$ , 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.

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

$\sqrt{700569} = 837$ $sqrt700569 = 837$

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