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Math Help - Rationalizing the denominator that is a cube root?

  1. #1
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    Rationalizing the denominator that is a cube root?

    I need help rationalizing the denominator if it is a cube root. I understand the if it is just a square root, you multiply it by itself. But im having trouble with rationalizing a cube root.
    Here is the problem i need help with:
    (3a)/(∛25a)
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  2. #2
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    Re: Rationalizing the denominator that is a cube root?

    Quote Originally Posted by Hibby21 View Post
    I need help rationalizing the denominator if it is a cube root. I understand the if it is just a square root, you multiply it by itself. But im having trouble with rationalizing a cube root.
    Here is the problem i need help with:
    (3a)/(∛25a)

    \frac{3a}{\sqrt[3]{25a}}\cdot\frac{\sqrt[3]{5a^2}}{\sqrt[3]{5a^2}}=~?
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  3. #3
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    Re: Rationalizing the denominator that is a cube root?

    \sqrt[3]{a}\sqrt[3]{a^2}= \sqrt[3]{a^3}= a.

    Or \sqrt[3]{a}\left(\sqrt[3]{a}\right)^2= (\sqrt[3]{a})^3= a.
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