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Math Help - Rationalizing denominators with cube roots

  1. #1
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    Rationalizing denominators with cube roots

     \sqrt[3]{5}
    ____
     \sqrt[3]{10}
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  2. #2
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    Quote Originally Posted by Tenskypoo View Post
     \sqrt[3]{5}
    ____
     \sqrt[3]{10}
    Hi

    \frac{\sqrt[3]{5}}{\sqrt[3]{10}} = \frac{5^{\frac{1}{3}}}{10^{\frac{1}{3}}} = \left(\frac{5}{10}\right)^{\frac{1}{3}} = \frac{1}{2^{\frac{1}{3}}} = \frac{1}{\sqrt[3]{2}} = \frac{2^{\frac{2}{3}}}{2} = \frac{\sqrt[3]{4}}{2}
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  3. #3
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    Quote Originally Posted by Tenskypoo View Post
     \sqrt[3]{5}
    ____
     \sqrt[3]{10}
    Cube root is a "third" of the number so you need two more:
    \sqrt[3]{10}\sqrt[3]{10}\sqrt[3]{10}= \left(\sqrt[3]{10}\right)^3= 10
    Multiply both numerator and denominator by \left(\sqrt[3]{10}\right)^2.
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