**Solution:**

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 = a^{2} + p - 2a√p

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

**Hence, √p + √q is irrational.**