# Thread:

1. ## 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

2. Originally Posted by NeedHelp18
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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