Question

Prove that each of the following numbers is irrational:

2 - √3

Answer 1

 Let 2 - √3 be rational. 

Hence, 2 and 2 - √3 are rational.

∴ (2 - 2 + √3) = √3 = rational [∵ Difference of two rational is rational] 

This contradicts the fact that √3 is irrational. 

The contradiction arises by assuming 2 - √3 is rational. 

Hence, 2 - √3 is irrational.