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.

Hint: square the surd and note the cross term may be simplified.
Also note that $\sqrt{3}/2 = \cos{(\pi/6)}$ and you may use the double angle formula $1 +\cos{t} = 2 \cos^2{(t/2)}$, etc.
