How to simplify this surd: $\sqrt{1+\frac{\sqrt{3}}{2}}+\sqrt{1-\frac{\sqrt{3}}{2}}$ $$\sqrt{1+\frac{\sqrt{3}}{2}}+\sqrt{1-\frac{\sqrt{3}}{2}} = x$$
We have to find the value of $x$. 
Taking the terms to other side and squaring is increasing the power of $x$ rapidly, and it becomes unsolvable mess.
I think the answer lies in simplification, but can't do it. Also I have tried taking $\sqrt{2}$ common, but it doesn't help.

Recognize the quantity under radical sign is a perfect square, it all cancels out.
$$\sqrt{1+\frac{\sqrt{3}}{2}}  = \sqrt{1+2\cdot \frac12 \cdot \frac{\sqrt{3}}{2}} = \sqrt { (\cos \pi/3 + \sin \pi/3 )^2} = (\cos \pi/3 + \sin \pi/3 ) $$
Similarly, 
$$\sqrt{1-\frac{\sqrt{3}}{2}}  = (\cos \pi/3 - \sin \pi/3 ) $$
Adding, $$ \rightarrow \sqrt 3 $$
