assume that is rational
⇒ = a/b, where a and b are integers.
⇒ √2 = 3a/b
we know that a, b and 3 are integers and they are also rational {i.e RHS is rational}
therefore √2 will be rational.
but we know that √2 is irrational.
there is a contradiction
so, is an irrational number.