Algebraic Brain Explosion

[Goldenboko]

So, I've got something I know will be included in a test tomorrow (the test isn't on it, but it's a little detail which will end up hurting me D: ).


Apparently fractions inside square roots are no-goes. So when you have something that looks like sqrt(1-sqrt(3)/2) you have to get rid of the two. My book ends up showing the answer as 1/2sqrt(2-sqrt(3)) Which confuses me, how did they simplify to get that?

If it helps here's the original question, "Use the half-angle formulas to determine the exact value of the sin 105 degrees".