Question

Prove that 5×√3 is irrational​

Answer 1

Answer:

✨ Answer ✨

$let \: be \: assume \: that \: 5 \sqrt{3} \\ is \: a \: rational \: number \\ \\ therefore \\ 5 \sqrt{3} = \frac{a}{b} \\ \\ \sqrt{3} = \frac{a}{5b} \\ \\ \frac{a}{5b} \: is \: a \: rational \: number \\ therefore \: \sqrt{3} \: is \: also \: a \: rational \: \\ number \: but \: it \: is \: contradict \: that \\ \sqrt{3} \: is \: irrational \: therefore \: our \\ assumption \: is \: wrong \: and \\ 5 \sqrt{3} \: is \: an \: irrational \: number.$