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Math Help - Rationalising a fourth root in the denominator

  1. #1
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    Rationalising a fourth root in the denominator

    Help! I've been stuck on this for a few days now. I can rationalize square roots in the denominator as well as terms with square roots, but I'm not sure where to begin with a fourth root. Should I multiply top and bottom by {\sqrt[4]{10}} or by {\sqrt[4]{1000}} or by something else?

    This is my problem:

    \frac{5-\sqrt10}{\sqrt[4]{10}}
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by MaddieKay View Post
    Help! I've been stuck on this for a few days now. I can rationalize square roots in the denominator as well as terms with square roots, but I'm not sure where to begin with a fourth root. Should I multiply top and bottom by {\sqrt[4]{10}} or by {\sqrt[4]{1000}} or by something else?

    This is my problem:

    \frac{5-\sqrt10}{\sqrt[4]{10}}
    I believe I'd multiply by \sqrt[4]{1000} to get that denominator to 10. Multiplying by \sqrt[4]{10} won't get the job done.
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  3. #3
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    \begin{gathered}<br />
\sqrt[4]{{10^3 }} = \left( {10} \right)^{\frac{3}<br />
{4}} \hfill \\<br />
\left[ {\left( {10} \right)^{\frac{1}<br />
{4}} } \right]\left[ {\left( {10} \right)^{\frac{3}<br />
{4}} } \right] = 10 \hfill \\ <br />
\end{gathered}
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  4. #4
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    Okay, I've worked through it and I come up with:

    \frac{\sqrt[4]{1000}-2\sqrt[4]{10}}{2}

    It gives me the same answer as the original equation when I plug it into my calculator, but is it in its simplest form?
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  5. #5
    Senior Member chella182's Avatar
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    Quote Originally Posted by Plato View Post
    \begin{gathered}<br />
\sqrt[4]{{10^3 }} = \left( {10} \right)^{\frac{3}<br />
{4}} \hfill \\<br />
\left[ {\left( {10} \right)^{\frac{1}<br />
{4}} } \right]\left[ {\left( {10} \right)^{\frac{3}<br />
{4}} } \right] = 10 \hfill \\ <br />
\end{gathered}
    I'd do this; multiply top and bottom by 10^(3/4).
    Also, how to do you big fractions like on your first post with the math function?
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