Question

Prove that number 3√3 are not rational.

Answer 1

Let us assume that 3√3 be a rational number.

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

Now, a/b =3√3

a/3b = √3

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

So, a/3b is a rational number

√3 is a rational number

But this contradicts to the fact that √3 is an irrational number.

Therefore, our assumption is wrong.

Hence, 3√3 is an irrational number.