Question

Given that √2 is irrational , prove that (5+3√2) is an irrational number

Answer 1

let
$5 + 3 \sqrt{2} = a \: rational \: number$
$so.....5 + 3 \sqrt{2} = a \div b$

soo...
$3 \sqrt{2} = a \div b - 5$
$3 \sqrt{2} = a - 5b \div b$
$\sqrt{2 } = a - 5b \div 3b$

since
$\sqrt{2} = rational \: number$
$5 + 3 \sqrt{2} \: is \: also \: a \: rational \: number$
hope it helps you