Question

Prove that of the numbers  ` 2 - sqrt(3)`  is irrational:

Answer 1

Let 2 - `sqrt (3)` be rational.
Hence, 2 and 2 - `sqrt (3)` are rational.

∴ (2 - 2 + `sqrt (3)`  ) = `sqrt (3)` = rational [∵ Difference of two rational is rational]
This contradicts the fact that  `sqrt (3)`  is irrational.
The contradiction arises by assuming 2 -  `sqrt (3)`  is rational.
Hence, 2 - `sqrt (3)` is irrational.