Prove that following numbers are irrational :

5 – √3

Let us assume 5 - is rational

5 - can be written in the form where a and b are co-prime.

Hence, 5 - =

- = – 5

- =

=-

Since, rational ≠ irrational

This is a contradiction.

, Our assumption is incorrect.

Hence, 5 - is irrational.