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Let \(n \in \mathbb{N}^*\). Show that \(\sqrt{n}\) is rational if and only if \(n\) is a perfect square. Hint. Suppose \(\sqrt{n} = p/q\) in irreducible form, then \(p^2 = n q^2\) and use Gauss / Euclid's lemma to show \(q = 1\).
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