Question

If p is a prime number, then prove that √p  is an irrational

Answer 1

Let p be a prime number and if possible,let  √p be rational

:.  √p  m/n where m and n are co-primes and n ≠ 0. 

Squaring on both sides, we get

Thus p is a common factor of m and n but this contradicts the fact that m and n are primes.

The contradiction arises by assuming that √p is rational. Hence, √p is irrational