Question

Prove that 3 + 2 under root 5 is irrational

Answer 1

Suppose \(\dfrac{\sqrt{5}}{5}\in \mathbb{Q}\), then \(\dfrac{\sqrt{5}}{5}=k\) for some \(k\in \mathbb{Z}\). So \(\sqrt{5}=5k\in \mathbb{Z}\) contradicting the fact that \(\sqrt{5}\in \mathbb{R}-\mathbb{Q}\).