In the proof of \(\sqrt{2}\), if a student ends the proof after only writing \(a\) is even, what is the error?

Correct answer: To obtain a contradiction, \(b\) must also be proved even

In the contradiction proof, we assume \(\sqrt{2}=a/b\), where \(a\) and \(b\) are coprime. The equation first shows that \(a\) is even; substituting this result back then shows that \(b\) is also even. Saying only that \(a\) is even does not contradict the coprime condition. The contradiction arises because both numbers would have 2 as a common factor. Exam tip: always state the final contradiction explicitly in a proof.