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Math Help - Rationalizing Trinomial Surds

  1. #1
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    Rationalizing Trinomial Surds

    How do I rationalize the follwoing trinomial surd ?

    \sqrt[3]{4} - \sqrt[3]{2} + 1
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  2. #2
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    Remember that

    \displaystyle \sqrt[3]{4} = \sqrt[3]{2 \times 2} = \sqrt[3]{2^2} = (\sqrt[3]{2})^2.


    So \displaystyle \sqrt[3]{4} - \sqrt[3]{2} + 1 = (\sqrt[3]{2})^2 - \sqrt[3]{2} + 1.


    This is a quadratic in \displaystyle \sqrt[3]{2}.
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  3. #3
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    But then , what will be the rationalizing factor of \sqrt[3]{4} - \sqrt[3]{2} + 1 ?
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  4. #4
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    Arka, [tex]a^3- b^3= (a+ b)(a^2- ab+ b^2)[/quote]
    Do you see that what you have is a^2- ab+ b^2? What are a and b?
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