Question

Prove 6+root 2 as irrational

Answer 1

Let, 6 + √2 be a rational number.

We know that 6 is a rational number.

Also, we know that

Rational - Rational = rational

=> (6 + √2 ) - 6 = Rational number

=> 6 - 6 + √2 = √2 = Rational number

But, √2 is an irrational number.

So, here our supposition gets wrong.

Hence, 6 + √2 will be a rational number.