Question

Consider the following statement. If m and n are any positive integers and mn is a perfect square, then m and n are perfect squares. Is the statement true or false

Answer 1

Answer:

False

Step-by-step explanation:

A number is said to be a perfect square if it is a product of some integer with itself.

Take two positive integers as $m=2\,,\,n=18$.

$mn=2(18)=36=6^2$

As $mn=6^2$, $mn$ is a perfect square.

But m and n are not perfect squares.

So, the given statement is false.