Question

Prove that 8+√2 is irrational

Answer 1

Let, 8 +√2 be a rational number.

We know that 8 is a rational number.

Also,

Rational - Rational = Rational

=> 8 + √2 - 8 = Rational

=> √2 = Rational

But, √2 is a rational number.

So, it contradicts our supposition.

Hence 8 +√2 is an irrational number.