Final answer:
To prove the statement, we use a direct proof by assuming that m and n are perfect squares, and then show that their product, m * n, is also a perfect square.
Step-by-step explanation:
To prove that if m and n are perfect squares, then m * n is also a perfect square, we can use a direct proof. Let m and n be perfect squares, which means there exist integers a and b such that m = a^2 and n = b^2. Now, we need to show that m * n is also a perfect square.
We can rewrite m * n as (a^2) * (b^2) which is equal to (a * b)^2. Since a * b is an integer, we can conclude that m * n = (a * b)^2 is a perfect square.
Therefore, if m and n are perfect squares, m * n is also a perfect square.
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