Prove that `sqrtp+sqrtq` is an irrational, where `p and q` are primes.

Explanation

Let us suppose that `sqrtp+sqrtq` is rational.
Again,let `sqrtp+sqrtq=a` where a is rationa.
Therefore, `sqrtq=a-sqrtp`
On squareing both sides, we get
`q=a^(2)+p-2asqrtp` `[therefore (a-b)^(2)=a^(2)+b^(2)-2ab]`
Therefore, `sqrtp=(a^(2)+p-q)/(2a)`, which is a contraction as the right hand side is rational number while `sqrtp` is irrational since p and are prime numbers/ Hence, `sqrtp+sqrtq` are prime numbers. Hence, `sqrtp and sqrtq` is irrational.