Question

Prove that following numbers are irrationals:

\[4 + \sqrt{2}\]

Answer 1

Let us assume that `4+sqrt2` is rational .Then , there exist positive co primes a and bsuch that

`4+sqrt2=a/b`

`sqrt2=a/b-4`

`sqrt=(a-4b)/b`

`sqrt2` is a rational numbers which is a contradication.

Hence \[4 + \sqrt{2}\] is irrational