You learn in algebra that $$\sqrt{ab}=\sqrt{a} \sqrt{b}$$ and that $$\sqrt{\frac ab}=\frac {\sqrt a}{\sqrt b}$$ You also learn to never make the fatal mistake of thinking $$\sqrt{a+b}=\sqrt{a}+\sqrt{b}$$
However, I am wondering if there is a rule for $\sqrt{a+b}$. I would think it would be pretty complex, if it exists at all.
$$\sqrt{a+b}=\text{?}$$