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Thread: Simplification of an equation

  1. #1
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    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
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  2. #2
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    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.
    Last edited by skeeter; Jul 1st 2012 at 12:21 PM.
    Thanks from Lepzed
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  3. #3
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    Re: Simplification of an equation

    Quote Originally Posted by Lepzed View Post
    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 $\displaystyle \sqrt{\left(1+\frac{\sqrt 3}{2} \right)}=\sqrt{\frac{1}{2}\left(2+\sqrt3\right)}$
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  4. #4
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    Re: Simplification of an equation

    Thanks for your very clear clarification
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