Question

Prove that + va is irrational, where p, q are primes​

Answer 1

Let us suppose that √p + √q is rational

. Let √p + √q = a, where a is rational

. => √q = a – √p

Squaring on both sides, we get

q = a2 + p - 2a√p => √p = (a2 + p - q)/2a, which is a contradiction as the right hand side is rational number, while √p is irrational.

Hence, √p + √q is irrational