Prove that is irrational.

Answer:

Consider,   be rational.

, where a, b are positive integers having no common factor other than 1

∴√3 =

Since a, b are non-zero integers, is rational.

Thus, equation shows that √3 is rational.

This contradicts the fact that √3 is rational.

The contradiction arises by assuming √3 is rational.

Thus,   is irrational.