Question

Prove that 7 root 5 is irrational

Answer 1

We can prove 7√5 irrational by contradiction.

Lets suppose that 7√5 is rational.

It means we have some co-prime integers a and b (b≠0) such that 7√5=ab

⇒√5=a7b ........ (1)

R.H.S of (1) is rational but we know that √5 is irrational.

⇒L.H.S≠R.H.S

⇒ Which means our assumption is wrong.

∴ 7√5 cannot be rational. Hence, it is irrational.

Hope this helps :)