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Math Help - Substitute suitable value of y to find 5^{1/3}

  1. #1
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    Substitute suitable value of y to find 5^{1/3}

    Given the equation (1+3y)^{\frac{1}{3}} \approx 1+y-y^2 is valid for |y|<\frac{1}{3}, by substituting a suitable value for y, find an approximate value of 5^{\frac{1}{3}} .

    I found the answer by substituting y=\frac{1}{5} and the answer is 1\frac{21}{29}

    But I dont understand why, when I used y=-\frac{4}{15}, i dont get the answer.

    Here are my workings.

    When y=-\frac{4}{15},

     (\frac{1}{5})^{\frac{1}{3}}\approx 1+\frac{-4}{15}-\frac{16}{225}=\frac{149}{225}

    Therefore, 5^{\frac{1}{3}}=\frac{225}{149} which is wrong
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  2. #2
    Newbie AgentSmith's Avatar
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    Re: Substitute suitable value of y to find 5^{1/3}

    \sqrt[3]{5} \approx 1.709 and \frac{149}{225} \approx 1.510.

    They are almost equal.
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  3. #3
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    Re: Substitute suitable value of y to find 5^{1/3}

    Quote Originally Posted by AgentSmith View Post
    \sqrt[3]{5} \approx 1.709 and \frac{149}{225} \approx 1.510.

    They are almost equal.
    In my opinion, they differ very much because if y=\frac{1}{5} is used instead, the answer is 1.72 which is very much closer to the exact answer. The problem over here is that I don't understand why such a huge difference was generated when it seemed all reasonable to use y=-\frac{4}{15}
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: Substitute suitable value of y to find 5^{1/3}

    Quote Originally Posted by Punch View Post
    I found the answer by substituting y=\frac{1}{5} and the answer is 1\frac{21}{29} But I dont understand why, when I used y=-\frac{4}{15}, i dont get the answer.
    Because 1/5 is closer to 0 than -4/15 .
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