Question

Prove that following number is irrational:

`5sqrt(2)`

Answer 1

Let us assume that \[5\sqrt{2}\]  is rational. Then, there exist positive co-primes a and bsuch that

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

`sqrt2=a/b-5`

`sqrt5=(a-5b)/b`

`sqrt2` is a rational which is a contradication