Question

prove that is a irrational number
$6 + \sqrt{2}$

Answer 1

Let
6 + √2 be a rational number.
Also,
we know that 6 is a rational number so,

Rational number - Rational number = Rational number.

=> ( 6 + √2 ) - 6

=> 6 - 6 + √2

=> √2

Clearly, √2 is irrational.

So here we contradicts our supposition.

Hence given number is irrational.

Answer 2

Hope this answer helps you.