Question

prove that 2+√2 is not a rational number

Answer 1

2+√2 = answer will not come because there in not an underoot of 2 so it is not a rational number.

Answer 2

Hello Mate!

$let \: x \: = 2 + \sqrt{2} \\ {x}^{2} = {(2 + \sqrt{2} )}^{2} \\ {x}^{2} = 4 + 2 + 4 \sqrt{2} \\ \frac{ {x}^{2} - 6 }{4} = \sqrt{2}$

Here, ( x^2 - 6 ) / 4 is rational which is equivalent to root 2 but we arrise at contradiction that root 2 is irrational.

Therefore,

$2 + \sqrt{2} \: is \: irrational \: no.$

Hope it helps☺!

A small message in the pic