(Q8).Prove that the following are irrational.

6 + √2

Let us suppose that 6 + √2 is a rational number.

∴ 6 + √2 =
p
q
 , q ≠ 0
⇒ √2 =
p
q
 -

⇒ √ = Difference of two rational numbers

⇒ So according to this, √ will be a rational number.

But this contradicts the fact that √2 is an number.

∴ Our supposition is wrong.

Hence 6 + √2 is an number.