Question

prove that 2+3√7 is a irrational no.​

Answer 1

$\large \bold{ \underline{ \underline{ \: To \: Prove : \: \: \: }}}$

$\to$ 2+3√7 is a irrational number

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

Let , 2 + 3√7 is an rational number

So ,

$\to 2 + 3 \sqrt{7} = \frac{a}{b}$

$\to 3 \sqrt{7} = \frac{a}{b} - 2$

$\to \sqrt{7} = \frac{a}{3b} - 2$

$\to \sqrt{7} = \frac{a - 3b}{3b}$

We know that , Irrational not equal to rational

Therefore , 2+3√7 is irrational number