Question

prove √7 + √2 is irrational

Answer 1

Let 2√7 be a rational number

2√7=p/q

p2q=√7

Hence p/2q is a rational number which says that √7 is a irrational number

Hence proved √7+√2 is a irrational number

Answer 2

Let's assume that

$\sqrt{7} + \sqrt{2} \: is \: a \: rational \: number \: \\ \\ \\ \\ \\\:$

such that (p /q is a rational number which is not equal to 0).

$\sqrt{7} + \sqrt{2} = \frac{p}{q}$

thus,

$\sqrt{2} = \frac{p}{q} - \sqrt{7}$

Therefore, if p/q is a rational number then

$\sqrt{2 } = \frac{p}{q} - \sqrt{7} \: is \: also \: a \: rational \: number$

But, sqrt 2 is an irrational number...

This contradicts our assumption that

$\sqrt{7} + \sqrt{2 \: } is \: a \: rational \: number$

Thus, it is an irrational number...

Hence, proved.....

Thank you...