Question

Prove that following numbers are irrationals:

\[5\sqrt{2}\]

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