Question

Prove that
$3 \sqrt{2} \:$
is irrational number

Answer 1

Let us assume that 3√2 is a rational number.
So,we can represent it in p/q form.
Let a and b be two co prime number such that
3√2=a/b
√2=a/3b

Clearly,3,a,b are integer
So,a/3b is a rational number and√2 is an irrational number.
Also,a rational number can never be equal to an irrational number.
So,we conclude that 3√2 is an irrational number.