Prove that is irrational.

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.