Say
3√ is rational. Then
3√ can be represented as
ab, where a and b have no common factors.
So 3=a2b2
and
3b2=a2. Now
a2 must be divisible by 3, but then so must a (fundamental theorem of arithmetic). So we have
3b2=(3k)2 and
3b2=9k2 or even
b2=3k2 and now we have a contradiction.
What is the contradiction?
