Prove that the following are irrational.

6 + √2

Let 6 + √2 be a rational number equal to , where a,b are positive co-primes. Then,

6 + √2 =

⇒ √2

⇒

Since a and b are integers, is also rational and hence, √2should be rational. This is contracdicts the fact that√2is irrational. Therefore , our assumption is false and hence, 6 + √2 is irrational.