Thread: 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

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:

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



Alternatively, prove this lemma: If , then .

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