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Math Help - adding radicals

  1. #1
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    adding radicals

    I don't know what to do for this one... the exponent outside the radical confuses me:

    \sqrt[3]{16} + 3\sqrt[3]{54}

    It says to simplify the expression. I know that I have to factor the numbers, but that exponent "3" is confusing. Help?
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  2. #2
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    Quote Originally Posted by isundae View Post
    I don't know what to do for this one... the exponent outside the radical confuses me:

    \sqrt[3]{16} + 3\sqrt[3]{54}

    It says to simplify the expression. I know that I have to factor the numbers, but that exponent "3" is confusing. Help?
    The same rules apply as when they are square roots. The only difference is now you have to find a CUBIC factor, rather than a square factor...

    Note that 16 = 8\cdot 2

    So \sqrt[3]{16} = \sqrt[3]{8\cdot 2} = \sqrt[3]{8}\cdot\sqrt[3]{2} = 2\cdot\sqrt[3]{2}.


    Also, note that 54 = 27\cdot 2.

    So \sqrt[3]{54} = \sqrt[3]{27\cdot 2} = \sqrt[3]{27}\cdot\sqrt[3]{2} = 3\cdot\sqrt[3]{2}.


    Therefore \sqrt[3]{16} + 3\cdot\sqrt[3]{54} = 2\cdot\sqrt[3]{2} + 9\cdot\sqrt[3]{2} = 11\cdot\sqrt[3]{2}.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    The same rules apply as when they are square roots. The only difference is now you have to find a CUBIC factor, rather than a square factor...

    Note that 16 = 8\cdot 2

    So \sqrt[3]{16} = \sqrt[3]{8\cdot 2} = \sqrt[3]{8}\cdot\sqrt[3]{2} = 2\cdot\sqrt[3]{2}.


    Also, note that 54 = 27\cdot 2.

    So \sqrt[3]{54} = \sqrt[3]{27\cdot 2} = \sqrt[3]{27}\cdot\sqrt[3]{2} = 3\cdot\sqrt[3]{2}.


    Therefore \sqrt[3]{16} + 3\cdot\sqrt[3]{54} = 2\cdot\sqrt[3]{2} + 9\cdot\sqrt[3]{2} = 11\cdot\sqrt[3]{2}.
    Oh, I see now. I forgot that I could take the equation apart, that makes it much easier

    Just wondering, where did the 9 come from? (in the last step)

    edit: Never mind, I see where it came from...

    Thanks for helping me!
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