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Math Help - proof that cuberoot 2 is not rational

  1. #1
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    proof that cuberoot 2 is not rational

    How would i prove that cuberoot 2 is not rational?

    Let cuberoot 2 be written in the form m/n, where m and n are coprime.
    So then m^3=2n^3
    Hence m^3 and thus m is divisible by 2
    So there exists integer k such that m=2k
    thus 8k^3 = 2n^3
    Thus n^3 = 4k^3

    Where do i go next? im stuck. Does it matter that its 4k^3 instead of say 2k^3? Can i just say that n^3 is thus even?
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  2. #2
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    Can't you continue as in the proof about \sqrt{2}? Namely, n^3=4k^3 implies that n is even and so m and n and not coprime.
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  3. #3
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    thanks! i got confused a bit because of the 4k^3 instead of a 2.
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