Question

Prove that 3+ root5 is irrational number ​

Answer 1

Hey

$let \: 3 + \sqrt{5} \: be \: a \: rational \: number \\ \\ = > 3 + \sqrt{5 } = \frac{p}{q} \\ \\ = > \sqrt{5} = \frac{p}{q} - 3 \\ \\ = > \sqrt{5} = \frac{p - 3q}{q }$

Here,LHS is irrational and RHS is rational so LHS≠RHS.

Our assumption is wrong.

Thus,3+√5 is an irrational

Henceforth,proved

Hope it helps you!!!