Question

Prove that following number is irrational:

\[\frac{3}{2\sqrt{5}}\]

Answer 1

Let us assume that 

\[\frac{3}{2\sqrt{5}}\] is rational. Then, there exist positive co primes a and b such that

\[\frac{3}{2\sqrt{5}}\] `=a/b`

`sqrt5=(3b)/(2a)`

Hence \[\frac{3}{2\sqrt{5}}\] is irrational

`sqrt5` is a rational numbers which is a contradication.