I ran into this issue with a trig identity, but the part I'm curious about is really just algebra, so I hope this is the right place for it.

At any rate, after doing the appropriate calculations I ended up with a formula of

$\displaystyle -\sqrt{3-2\sqrt{2}}$

the book, however, lists the answer as

$\displaystyle 1-\sqrt{2}$

The two are equivalent, I'm just curious as to the mechanism of converting from one to the other. Can someone explain it to me, if possible?