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Thread: 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 $\displaystyle {\sqrt[4]{10}}$ or by $\displaystyle {\sqrt[4]{1000}}$ or by something else?

    This is my problem:

    $\displaystyle \frac{5-\sqrt10}{\sqrt[4]{10}}$
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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 $\displaystyle {\sqrt[4]{10}}$ or by $\displaystyle {\sqrt[4]{1000}}$ or by something else?

    This is my problem:

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

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

    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
    $\displaystyle \begin{gathered}
    \sqrt[4]{{10^3 }} = \left( {10} \right)^{\frac{3}
    {4}} \hfill \\
    \left[ {\left( {10} \right)^{\frac{1}
    {4}} } \right]\left[ {\left( {10} \right)^{\frac{3}
    {4}} } \right] = 10 \hfill \\
    \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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