# How do I simplify a radical within a

How do I simplify a radical within a radical in this half-angle problem?
$\mathrm{sin}\left(-\frac{3\pi }{8}\right)=±\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}$
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Ouhamiptkg
First, $-\frac{\pi }{2}<-\frac{3\pi }{8}<0$ , so we're in the fourth quadrant and thus sine is negative here. Second:
$\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}$
$=\sqrt{\frac{\frac{2+\sqrt{2}}{2}}{2}}$
$=\sqrt{\frac{2+\sqrt{2}}{4}}$
$=\frac{\sqrt{2+\sqrt{2}}}{2}$