Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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

Advertisement Remove all ads

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/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.

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

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×