After a small search that I did I was unable to spot any answers here.What I am trying is to prove why the $2^{\sqrt2}$ is transcendental number. I know that this probably is a closed problem and probably many people have proved it already,but I want to reach the answer by myself after doing a research on this problem and going through several books and sources and test my knowledge and my power.So what I basically need is to give me guideline to solve the problem.If my question is too general,before you close it,please give me some information to rephrase,so it won't be so general.



Guidelines to prove that $2^{\sqrt{2}}$ is a transcendental number?
By the [Gelfond–Schneider theorem](http://en.wikipedia.org/wiki/Gelfond%27s_theorem), $2^{\sqrt2}$ is transcendental.


$2^{\sqrt 2}$ is called the [Gelfond–Schneider constant](https://secure.wikimedia.org/wikipedia/en/wiki/Gelfond%E2%80%93Schneider_constant).


See also <https://math.stackexchange.com/questions/173804/deciding-whether-2-sqrt2-is-irrational-transcendental>


