Question

show that 3√2 /5 is an irrational number.​

Answer 1

$\large \bold{ \underline{ \underline{ \: Solution : \: \: \: }}}$

Let us assume , 3√2/5 is an rational number

$\to \frac{3 \sqrt{2} }{5} = \frac{a}{b} \\ \\ \to \sqrt{2} = \frac{5a}{3b}$

Since 3 , a and b are integers , 5a/3b is rational and so √2 Is rational

But this contradicts the fact that √2 is irrational

So , we concluded that 3√2/5 is irrational