Lower bound on $ \chi(G) $ + $ \chi(G') $

Question

I am trying to prove that $ 2\sqrt{n} $ $ \leq $ $ \chi(G) $ + $ \chi(G') $.
My guess is to try squaring both sides. I know that $ \chi(G) $ + $ \chi(G') $ is $ \leq $ n + 1. Here n is number of vertices in G. Somehow use that inquality to get the answer. But then I do not know how to bound $ \chi(G) $ * $ \chi(G') $ Here $ \chi(G) $ is the chromatic number of G, G' is the complement of G