Question

prove that 2√3 is irrational

Answer 1

let assume that
$2 \sqrt{3}$
be rational no than it can be written in form of

$2 \sqrt{3} = a \div b$
where a & b are coprime no.
$\sqrt{3 } = a \div 2b$
$a \div 2b = rational \: no$


but we know that
$\sqrt{3 } = irratonal \: no \:$
it contradicts our assumption so
$2 \sqrt{3} \: is \: irrational \: no$