A student assumes that \(\sqrt{3}\) can be written as \(\frac{a}{b}\) in lowest terms. During the proof, it is found that 3 divides both \(a\) and \(b\). Which conclusion about the student’s assumption is correct?

Correct answer: It contradicts the claim that \(\frac{a}{b}\) is in lowest terms; therefore, \(\sqrt{3}\) is irrational.

If 3 divides both \(a\) and \(b\), then \(\frac{a}{b}\) is not in lowest terms. This contradicts the original assumption, so \(\sqrt{3}\) is irrational. Exam tip: look for a common factor in numerator and denominator.