Question

Prove that following numbers are irrationals:

\[\frac{2}{\sqrt{7}}\]

Answer 1

(i) Let us assume that `2/sqrt7` is rational .Then , there exist positive co primes a and b such that

`2/sqrt7=a/b`

`sqrt7=(2b)/a`

`sqrt7`is rational number which is a contradication.

Hence `2/sqrt7` is irrational