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Math Help - I just don't understand radicals:

  1. #1
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    I just don't understand radicals:

    How does
    -(\frac{\sqrt{3}}{6}) - (\frac{\sqrt{3}}{3}) = -(\frac{\sqrt{3}}{2})

    Here's my work:
    -(\frac{\sqrt{3}}{6}) - (\frac{\sqrt{3}}{3})
    -(\frac{\sqrt{3}}{6}) - (\frac{2}{2}*\frac{\sqrt{3}}{3})
    -(\frac{\sqrt{3}}{6}) - (2*\frac{\sqrt{3}}{6})
    -(\frac{\sqrt{3}}{6})

    I get so confused when I have to manipulate radicals. Any ideas on what I can do to fix it?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    The line before last ... check again!
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  3. #3
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    -(\frac{\sqrt{3}}{6}) - (2*\frac{\sqrt{3}}{6}) BAD...

    Actually, I think I mistyped it into the forum. [edit] Even though I mistyped it, I think it is still the same. I'm not sure where I'm going wrong with it. Is there a 'radical tutorial' website that'll be helpful?[/edit]

    -(\frac{\sqrt{3}}{6}) - (\frac{2\sqrt{3}}{6})
    -(\frac{\sqrt{3}}{6})


    I know the denominator should eventually be a 2, but I just do see that happening at any time of simplifying the solution.
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  4. #4
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    Quote Originally Posted by EMyk01 View Post
    -(\frac{\sqrt{3}}{6}) - (2*\frac{\sqrt{3}}{6}) BAD...

    Actually, I think I mistyped it into the forum. [edit] Even though I mistyped it, I think it is still the same. I'm not sure where I'm going wrong with it. Is there a 'radical tutorial' website that'll be helpful?[/edit]

    -(\frac{\sqrt{3}}{6}) - (\frac{2\sqrt{3}}{6})
    -(\frac{\sqrt{3}}{6})


    I know the denominator should eventually be a 2, but I just do see that happening at any time of simplifying the solution.
    -\left(\frac{\sqrt{3}}{6}\right)-2\left(\frac{\sqrt{3}}{6}\right)=(-1-2)\frac{\sqrt{3}}{6}=how\ many\ \frac{\sqrt{3}}{6}\ ?
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  5. #5
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    Quote Originally Posted by Archie Meade View Post
    -\left(\frac{\sqrt{3}}{6}\right)-2\left(\frac{\sqrt{3}}{6}\right)=(-1-2)\frac{\sqrt{3}}{6}=how\ many\ \frac{\sqrt{3}}{6}\ ?

    Okay, I think I understand. You were able to pull out the -1 and the -2 from the \frac{\sqrt{3}}{6}

    In doing so, I have -3*\frac{\sqrt{3}}{6}

    Then solving the rest of the problem, it should look like:

     \frac{-3}{1}(\frac{\sqrt{3}}{6})

    -3 and 6 cancel out and I get my final answer of:
    -\frac{\sqrt{3}}{2}

    Is that correct?

    [edit] I seem to have a hard time doing this latex coding stuff. Please excuse me while I try to fix it.
    [edit again] Okay, hopefully that fixed it.
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  6. #6
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    Quote Originally Posted by EMyk01 View Post
    Okay, I think I understand. You were able to pull out the -1 and the -2 from the \frac{\sqrt{3}}{6}

    In doing so, I have -3*\frac{\sqrt{3}}{6}

    Then solving the rest of the problem, it should look like:

     \frac{-3}{1}\left(\frac{\sqrt{3}}{6}\right)

    -3 and 6 cancel out and I get my final answer of:

    -\frac{\sqrt{3}}{6}

    Is that correct?
    But you were wondering why the answer should be -\frac{\sqrt{3}}{2}

    -3\frac{\sqrt{3}}{6}=-\frac{3}{6}\sqrt{3}=?
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  7. #7
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    That was one of those mistakes that I fixed in the process. I said, "-3 and 6 cancel out" but in the math, I didn't cancel it out. So I now have the edited version,  -\frac{\sqrt{3}}{2} which is the end answer that I was looking for. I think I'm finished now...
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  8. #8
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    Ah! sorry... yes, Latex takes getting used to at the beginning. Use "Preview" until you're ready to post.
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