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

(m,n) = (3, 27)

The statement is false. Counterexample: Let m and n be the numbers in the ordered pair above. Then mn is a perfect square and at least one of m and n is not a perfect square.

Explanation:

3 * 27 = 81

Answer 2

False

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.