Question

Prove that the following number is irrational.

`2 + sqrt(3)`

Answer 1

To prove:

`2 + sqrt(3)` is irrational

Proof by Contradiction:

Let `2 + sqrt(3)` be rational

Then:

⇒ `sqrt(3) = (2 + sqrt(3)) - 2`

⇒ `sqrt(3)` = rational number − 2 = rational

But this contradicts the known fact that `sqrt(3)` is irrational.