# Prove that 1/Sqrt (3) is Irrational. - Mathematics

Prove that 1/sqrt (3) is irrational.

#### Solution

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/ais 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.

Concept: Concept of Irrational Numbers
Is there an error in this question or solution?