Demonstrate that if $ {\sqrt{a}} + {\sqrt{b}}\in\mathbb{Q}$ then $ {\sqrt{a}}\in\mathbb{Q}$ and ${\sqrt{b}}\in\mathbb{Q}$ $a,b\in\mathbb{Q}$ 
if $$ {\sqrt{a}} + {\sqrt{b}}\in\mathbb{Q}$$
demonstrates: $$ {\sqrt{a}}\in\mathbb{Q}$$
              $${\sqrt{b}}\in\mathbb{Q}$$ 
I try to solve it with the property:
If x, y $\in\mathbb{Q}$ then x + y $\in\mathbb{Q}$ and xy $\in\mathbb{Q}$

Hint: If $\sqrt{a}+\sqrt{b}=r$, then $\sqrt{a} = \dfrac{r^2+a-b}{2r}$.
