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^sprt{2} 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.
closed as off topic by Charles, unknown (google), Victor Protsak, Henry Cohn, Todd Trimble♦ Sep 24 '12 at 18:27Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question. 


By the Gelfond–Schneider theorem, $2^{\sqrt2}$ is transcendental. $2^{\sqrt 2}$ is called the Gelfond–Schneider constant. See also http://math.stackexchange.com/questions/173804/decidingwhether2sqrt2isirrationaltranscendental 


Don't worry, your question is wellstated. Some of these simply stated questions about transcendental numbers are still unknown! I don't know about this one. But here is another: Is $\pi^\pi$ a rational number? This one was unknown 20 years ago, and I expect it is still unknown. 

