8. Prove that

Solution:

Let’s assume on the contrary that

   

is a rational number. Then, there exist co prime positive integers a and b such that

   

⇒

   

⇒

   

⇒

   

is rational [∵

   

, a and b are integers ∴

   

is a rational number]

This contradicts the fact that

   

is irrational. So, our assumption is incorrect.

Hence,

   

is an irrational number.