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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.

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closed as off topic by Charles, unknown (google), Victor Protsak, Henry Cohn, Todd Trimble Sep 24 '12 at 18:27

Questions 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.

up vote 6 down vote accepted

By the Gelfond–Schneider theorem, $2^{\sqrt2}$ is transcendental.

$2^{\sqrt 2}$ is called the Gelfond–Schneider constant.

See also

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Thank you for your valuable help.Now at least I know where I can find the answer and what to look for to gain more knowledge. – el10780 Sep 24 '12 at 19:39

Don't worry, your question is well-stated. 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.

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Oh thank God.I am not experienced like you guys here.Thanks for your reply and thanks for giving me another problem to think about.(Although I do not think I will something like that.0 :) One think I can't understand though.Why they closed this question.The users who closed it claimed that it is off-topic.Off-topic compared to what?Did I misused the tagging? – el10780 Sep 24 '12 at 19:38
@el10780, this site is for research-level questions. For other questions, see . – lhf Sep 25 '12 at 2:25
Ok.Thank you for your respond and I apologize for my ignorance. – el10780 Sep 25 '12 at 5:39

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