Simplification of an equation

I'm reading through some worked examples in a book and stumbled upon this one:

$\displaystyle \sqrt(\frac{1}{2}(1 - \frac{1}{2}\sqrt(3)) = \frac{1}{2}\sqrt(2 - \sqrt(3))$

I can't quite see to get there, could someone clarify this a bit? Would be a tremendous help :)

Re: Simplification of an equation

$\displaystyle \sqrt{\frac{1}{2}\left(1 - \frac{\sqrt{3}}{2}\right)}}$

$\displaystyle \sqrt{\frac{1}{2} - \frac{\sqrt{3}}{4}\right)}}$

$\displaystyle \sqrt{\frac{2}{4} - \frac{\sqrt{3}}{4}}$

$\displaystyle \sqrt{\frac{2 -\sqrt{3}}{4}}}$

$\displaystyle \frac{\sqrt{2 - \sqrt{3}}}{\sqrt{4}}$

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

fyi, this is an expression, not an equation.

Re: Simplification of an equation

Quote:

Originally Posted by

**Lepzed** I'm reading through some worked examples in a book and stumbled upon this one:

$\displaystyle \sqrt(\frac{1}{2}(1 - \frac{1}{2}\sqrt(3)) = \frac{1}{2}\sqrt(2 - \sqrt(3))$

Perhaps writing correctly would help.

$\displaystyle \sqrt{\frac{1}{2}\left(1+\frac{\sqrt3}{2}\right)}= \sqrt{\frac{1}{2}}\sqrt{\left(1+\frac{\sqrt 3}{2} \right)}$

Now note that $\displaystyle \sqrt{\left(1+\frac{\sqrt 3}{2} \right)}=\sqrt{\frac{1}{2}\left(2+\sqrt3\right)}$

Re: Simplification of an equation

Thanks for your very clear clarification :)