Question

Prove that (3-√5)is irrational

Answer 1

Hey!

First of all let us assume that3 -root 5 is a rational numbers so,

$3 - \sqrt{5 } = \frac{a}{b}$

$\sqrt{5 } = \frac{a}{b} - \frac{3}{1}$

$\sqrt{5} = \frac{a - 3b}{b}$

here a ,3b and b are integers and the whole fraction is rational which is equal an irrational number so we know that this is wrong so , hence we have to change our assumption.

therefore

$3 - \sqrt{5}$

is an irrational number.

I hope this answers your question!