Fun radicals problem?

http://www.futilitycloset.com/2012/08/22/a-simple-proof/

Can an irrational number to an irrational power be a rational number?

Yes. sqrt 2 ^ sqrt 2 is either rational or irrational. If it’s rational then our task is done. If it’s irrational, then (sqrt 2 ^ sqrt 2) ^ sqrt 2 = 2 proves the statement.

 

 

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