whats the easiest way to do this? i have never done this type of problem before

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- Mar 23rd 2009, 05:33 PMNeedHelp18How 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

- Mar 23rd 2009, 06:01 PMJhevon
the easiest way?

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

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

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

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