Substituting (√3)/2 into √(1±x), for x, may not look like it has much potential to be simplified, but it can be simplified quite nicely.

$\displaystyle \sqrt{1\pm\frac{\sqrt{3}\,}{2}\,}=\sqrt{\frac{4\pm 2\sqrt{3}\,}{4}\,}$$\displaystyle =\frac{\sqrt{4\pm2\sqrt{3}\,}}{2}}$

$\displaystyle =\frac{\sqrt{3+1\pm2\sqrt{3}\,}}{2}}$

$\displaystyle =\frac{\sqrt{(\sqrt{3})^2\pm2\sqrt{3}\,+1}}{2}}$

$\displaystyle =\frac{\sqrt{\left(\sqrt{3}\pm1\right)^2}}{2}}$

$\displaystyle =\frac{\sqrt{3}}{2}\pm1$

This should make plugging in $\displaystyle \frac{\sqrt{3}}{2}$ for x much easier.