Question

Prove that following number is irrational:

`2/sqrt(7)`

Answer 1

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.