Question

prove that 5√3 is an irrational number.​

Answer 1

Let us assume

$5 \sqrt{3 } \: \: \: is \: not \: a \: irrational \: no.$

.: It is a rational no.

.:

$5 \sqrt{3} \: = \frac{p}{q}$

$\sqrt{3} = \frac{p}{5q}$

Therefore from above it is proved that under root 3 is rational no.

But it contradicts the fact that

Under root 3 is irrational no.

.: the assumption was incorrect and 5 root 3 is an irrational no.