anonymous one year ago Prove that 3 + 2 under root 5 is irrational

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1. zzr0ck3r

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 $$\sqrt{5}\in \mathbb{R}-\mathbb{Q}$$.