Prove that is irrational, where p, q are primes.

Let √p + √qbe rational

⇒ √p + √q [where a, b are co-primes and integers]

Squaring both sides

⇒

⇒

⇒ 2√pq = a^2/b^2 -p-q

⇒

⇒ ….I

∴ from Eq. I our assumption contradicts here, because p is rational

Hence, √p + √q is irrational number.