Question

Prove that 5+3V2 is an irrational number.​

Answer 1

Lets assume that 5+3√2 is rational and of the form a/b, where a and b are co-prime.

5+3√2=a/b

3√2=a/b-5

 √2=a/3b-5/3

Since a and b are integers, the RHS is rational. So, √2 is also rational. But this contradicts the fact that √2 is irrational. So our assumption is wrong.

So, 5+3√2 is irrational.