Question

Prove that $\sqrt{7}$ is an irrational number.

Answer 1

We have to prove that is an irrational number

We will prove this by contradiction:

Let be an irrational number such that where x and y are co prime

So’

This means that:

From equation (1) and (2) we see that 7 is a common factor of x and y. This contradicts the fact that x and y have no common factor

Hence is an irrational number.