Prove that following numbers are not rational :

3√3

Let us assume that 3 be a rational number.

Then, it will be of the form where a and b are co-prime and b≠0.

Now, =3

=

Since, a is an integer and 3b is also an integer (3b ≠ 0)

So, is a rational number

is a rational number

But this contradicts to the fact that is an irrational number.

Therefore, our assumption is wrong.

Hence, 3 is an irrational number.