Which option shows the correct cause-effect relation used in the proof of \(\sqrt{3}\)?

Correct answer: If \(3\mid p^2\), then \(3\mid p\); hence \(p=3k\), where \(k\) is an integer.

Option A gives the correct relation. Since 3 is prime, if \(p^2\) is divisible by 3, then \(p\) must also be divisible by 3. Therefore, we can write \(p=3k\), where \(k\) is an integer. In the irrationality proof of \(\sqrt{3}\), this ultimately shows that \(q\) is also divisible by 3, contradicting the assumption that \(p\) and \(q\) are coprime. Exam tip: For a prime \(r\), remember that \(r\mid a^2\) implies \(r\mid a\).