Question

Prove that `1/sqrt (3)` is irrational.

Answer 1

Let  `1/sqrt (3)`  be rational.
∴  `1/sqrt (3) = a/b` , where a, b are positive integers having no common factor other than 1
∴` sqrt(3) = b/a`                        ….(1)
Since a, b are non-zero integers, `b/a`is rational.
Thus, equation (1) shows that `sqrt (3)` is rational.
This contradicts the fact that `sqrt(3)` is rational.
The contradiction arises by assuming `sqrt(3)` is rational.

Hence, `1/sqrt (3)` is irrational.