Question
Prove that following numbers are irrationals:
$\frac{3}{2\sqrt{5}}$
$\frac{3}{2\sqrt{5}}$
✓
Answer
Let us assume that $\frac{3}{2\sqrt{5}}$ is rational. Then, there exist positive co-primes a and b such that, $\frac{3}{2\sqrt{5}}=\frac{\text{a}}{\text{b}}$ $\sqrt{5}=\frac{3}{2}\frac{\text{b}}{\text{a}}$ $\sqrt{5}$ is rational. This is a contradication.Thus $\frac{3}{2\sqrt{5}}$ is irrational.
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