1. The problem statement, all variables and given/known data if a and b are irrational numbers, is a^b necessarily an irrational number ? prove it. 3. The attempt at a solution this is an question i got from my first maths(real analysis) class (college) , and have to say, i have only little knowledge about rational number, i would like to give it a try to find a solution but need some help, i know that a^b is not necessarily an irrational number cause if a = √2^√2 and b = √2 it becomes rational. but i don't think its the proof that the question is expecting as its on real analysis. any help would be greatly appreciated and sorry for my English too.