Question

Prove that 3√3 is irrational number.​

Answer 1

Step-by-step explanation:

Since both q and r are odd, we can write q=2m−1 and r=2n−1 for some m,n∈N.

We note that the lefthand side of this equation is even,

while the righthand side of this equation is odd, which is a contradiction.

Therefore there exists no rational number r such that r2=3. Hence the root of 3 is an irrational number

Answer 2

Let us assume that 3−3 is a rational number

Then. there exist coprime integers p, q,q=0 such that 

     3−3=qp

=>3=3−qp

Here, 3−qp is a rational number, but 3 is an irrational number.

But, an irrational cannot be equal to a rational number.This is a contradiction.

Thus, our assumption is wrong.

Therefore 3−3 is an irrational number.