Prove that 3√2 is irrational.
Let us assume, to the contrary, that 3√2 is
rational. Then, there exist co-prime positive integers a and b such that
3√2=ab
⇒ √2=a3b
⇒ √2 is rational ...[∵3,a and b are integers∴a3bis a rational number]
This contradicts the fact that √2 is irrational.
So, our assumption is not correct.
Hence, 3√2 is an irrational number.