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Math Help - How to prove that cube root of 5 is not rational number

  1. #1
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    How to prove that cube root of 5 is not rational number

    whats the easiest way to do this? i have never done this type of problem before
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by NeedHelp18 View Post
    whats the easiest way to do this? i have never done this type of problem before
    the easiest way?

    consider the roots of the polynomial: x^3 - 5 = 0

    Now apply the rational roots theorem. What can you come up with?



    Alternatively, prove this lemma: If 5 | x^3, then 5 | x.

    then apply the technique used here in post #2

    it is a longer, more sophisticated proof, but it is the conventional one, and certainly one you should know, for historical and aesthetic reasons at least
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