If $\displaystyle \sqrt{a + b} = \sqrt{a} + \sqrt{b}$, which of the following must be true?

A. $\displaystyle a = b$

B. $\displaystyle a = 0 $ and $\displaystyle b = 0$

C. $\displaystyle a = 0 $ or $\displaystyle b = 0$

D. $\displaystyle a + b > 1$

E. $\displaystyle a = 1$ and $\displaystyle b > 0$

I mean clearly C works but why don't the other choices work?