Question

show that 3√5 is an irrartional number

Answer 1

yes it is a irrational number because it is not in p/q form

Answer 2

we know that √5 is irrational and it cannot be represented in the form of a/b.
let us assume that 3√5 is rational,so it can be represented in the form a/b
$3 \sqrt{5} = \frac{a}{b} \\ \sqrt{5} = \frac{a}{3b} \\ here \: \sqrt{5 } = \frac{a}{b}$
but we know that ,it is not possible.that means our assumption is wrong .
so 3√5 irrational.