# [SOLVED] simplification problem

• Oct 24th 2009, 09:32 AM
satis
[SOLVED] simplification problem
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?
• Oct 24th 2009, 09:43 AM
skeeter
Quote:

Originally Posted by satis
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?

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

$\displaystyle -\sqrt{2 - 2\sqrt{2} + 1}$

$\displaystyle -\sqrt{(\sqrt{2} - 1)^2}$

$\displaystyle -|\sqrt{2}-1|$

$\displaystyle 1 - \sqrt{2}$
• Oct 24th 2009, 09:50 AM
satis
ah, it's just a matter of factoring it. Thank you, totally missed that.