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Math Help - Cube Root times Cube Root

  1. #1
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    Cube Root times Cube Root

    cube root of 16(m^2)(n) multiplied by cube root of 27(m^2)(n)

    I converted the problem to (16m^2n)^1/3 * (27m^2n)^/3.

    Is this the correct way to write the original problem another way?

    I finally got (432m^4n^2)^2/3.

    Is this correct?
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  2. #2
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    Quote Originally Posted by sharkman View Post
    cube root of 16(m^2)(n) multiplied by cube root of 27(m^2)(n)

    I converted the problem to (16m^2n)^1/3 * (27m^2n)^/3.

    Is this the correct way to write the original problem another way?

    I finally got (432m^4n^2)^2/3.

    Is this correct?
    Nearly there. Recall that \sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{ab}

    In your question you have \sqrt[3]{16(m^2)(n)} \times \sqrt[3]{27(m^2)(n)}.

    Using the fact I gave first, this means than the answer is...

    Hint: Your multiplication of the m and n terms was not wrong, it was the index - \frac{2}{3} - that you got wrong.
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  3. #3
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    answer...

    Quote Originally Posted by craig View Post
    Nearly there. Recall that \sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{ab}

    In your question you have \sqrt[3]{16(m^2)(n)} \times \sqrt[3]{27(m^2)(n)}.

    Using the fact I gave first, this means than the answer is...

    Hint: Your multiplication of the m and n terms was not wrong, it was the index - \frac{2}{3} - that you got wrong.
    The answer should be cubert{432m^4n^2}, right?
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  4. #4
    Super Member craig's Avatar
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    Correct
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  5. #5
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    great

    Quote Originally Posted by craig View Post
    Correct
    Great! Thanks!
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  6. #6
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    Quote Originally Posted by sharkman View Post
    The answer should be cubert{432m^4n^2}, right?
    Don't be too shocked if your teacher marks it wrong because it has not been simplified as much as it could be. m^4= m^3 m so \sqrt[3]{m^4}= \sqrt[3]{m^3}\sqrt[3]{m}= m\sqrt[3]{m}. Perhaps more importantly, 432= (16)(27)= (2^4)(3^3)= (2^3)(3^3)(2) so \sqrt[3]{432}= \sqrt[3]{2^3}\sqrt[3]{3^3}\sqrt[3](2)= 6\sqrt[3]{2}.

    The best way to write your answer is 6m\sqrt[3]{2mn^2}.
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  7. #7
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    ok

    Quote Originally Posted by HallsofIvy View Post
    Don't be too shocked if your teacher marks it wrong because it has not been simplified as much as it could be. m^4= m^3 m so \sqrt[3]{m^4}= \sqrt[3]{m^3}\sqrt[3]{m}= m\sqrt[3]{m}. Perhaps more importantly, 432= (16)(27)= (2^4)(3^3)= (2^3)(3^3)(2) so \sqrt[3]{432}= \sqrt[3]{2^3}\sqrt[3]{3^3}\sqrt[3](2)= 6\sqrt[3]{2}.

    The best way to write your answer is 6m\sqrt[3]{2mn^2}.
    I understand. You decided to break the problem down a bit more.
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