Question

Prove that (2 + √3) is irrational.

Answer 1

Let (2 + √3) be rational. 

Then, both (2 + √3) and 2 are rational. 

∴ { (2 + √3) – 2 } is rational [∵ Difference of two rational is rational] 

⇒ √3 is rational. 

This contradicts the fact that √3 is irrational. 

The contradiction arises by assuming (2 + √3) is rational. 

Hence, (2 + √3) is irrational.