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?