Prove that 3√3 is not a rational number.

Let 3√3 be a rational number say r .
Then 3√3 =  r
√3 = (1/3) r
(1/3) r is a rational number because product of two rational number is a rational number.
=>√3 is a rational number but √3 is not a rational number.
Therefore our assumption 3√3 is a rational number is wrong.