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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

2 Answers

14 votes

Answer:

(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

User Waqas Javed
by
8.8k points
2 votes

Answer:

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.

User Zsolt Szilagyi
by
8.3k points

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