Question

Prove that the following number is irrational.

`3 - sqrt(5)`

Answer 1

To Prove:

`3 - sqrt(5)` is irrational

Proof by Contradiction:

Let `3 - sqrt(5)` be rational

Then:

⇒ `sqrt(5) = 3` – (rational number) = rational

But we know:

`3 - sqrt(5)` is irrational