Question

prove that 2-3√5 is irrational

Answer 1

Let x=2−3 √5 be a rational number.

3√5 =2−x

√5 = $\frac{2 - x}{3}$

Since x is rational, 2-x is rational and hence $\frac{2 - x}{3}$ is also rational number

$⇒$ √5 is a rational numbers, which is a contradiction.

Hence 2−3 √5 must be an irrational number.