Prove that

Let  is a rational number.
we can find two co-prime numbers  p, q (q ≠ 0) such that
Let ‘p’ and ‘q’ have a common factor other than 1.
Therefore, p² is divisible by 5 and it can be said that ‘p’ is divisible by 5.
Let p = 5k, where k is an integer
(5k)² = 5q² this mean that q² is divisible by 5 and hence, q is divisible by 5.
q² = 5k² this implies that p and q have 5 as a common factor.
And this is a contradiction to the fact that p and q are co-prime.
Hence,  cannot be expressed as  or it can be said that  is irrational.