Reema says, “The decimal expansion of \(\sqrt{3}\) is infinite, so it is irrational.” What is the flaw in her reasoning?

Correct answer: An infinite decimal expansion alone does not prove irrationality; it may be recurring, as in \(1/3\)

An infinite decimal alone does not imply irrationality: \(1/3=0.333\ldots\) is rational. For \(\sqrt{3}\), assume \(p/q\) is in lowest terms; the proof shows that both \(p\) and \(q\) are divisible by 3, a contradiction. Exam tip: distinguish non-terminating recurring decimals from non-recurring decimals.