Final answer:
To prove that if n is a perfect square, then n^2 is not a perfect square, we can use proof by contradiction. Assume that n^2 is a perfect square and derive a contradiction by showing that n is also a perfect square. Therefore, our assumption is false, and it is proven that if n is a perfect square, then n^2 is not a perfect square.
Step-by-step explanation:
To prove that if n is a perfect square, then n2 is not a perfect square, we can use proof by contradiction.
Let's assume that n2 is a perfect square. So, there exists some positive integer k such that n2 = k2.
By taking the square root on both sides, we get n = k. This means n is also a perfect square.
However, this contradicts our assumption that n is a perfect square, since we assumed n is not a perfect square initially. Therefore, our assumption is false, and it is proven that if n is a perfect square, then n2 is not a perfect square.