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Math Help - Prove that the number 2^(1/3)+3^(1/2) is algebraic

  1. #1
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    Prove that the number 2^(1/3)+3^(1/2) is algebraic

    Hey, i'm having trouble on how to tackle this question "Prove that the number 2^(1/3)+3^(1/2) is algebraic"
    I know i have to show it as a polynomial but I don't know where to begin.
    Any help would be appreciated

    Thanks
    Last edited by peterty; November 19th 2013 at 05:52 AM.
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  2. #2
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    Re: Prove that the number 2^(1/3)+3^(1/2) is algebraic

    Let x=2^{1/3}+3^{1/2}. Then for any positive integer n, the number x^n is a linear combination with rational coefficients of some fixed numbers \{a_1,\dots,a_k\}. Find these a_k, and, in particular, k. This means that k + 1 numbers 1=x^0, x, x^2, ..., x^k are linearly dependent over \mathbb{Q}. What does this mean?

    Edit: I did not notice that this is a pre-university forum, so you may not know about linear dependence. Please say if the description above makes sense to you.
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