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I remember someone once asked about checking the equality of equations like, Sqrt(5-2*Sqrt(6))=Sqrt(3)-Sqrt(2) in Mathemaica. "FullSimplify" is a good solution. After reading Edward R. Scheinerman's article "When Close Enough Is Close Enough" published on American Math Monthly June-July 2000, I know how to check equality "manually" if FullSimplify happens to fail. I implement a function in Mathematica according to Scheinerman's theory. I recommend you read his original paper if possible. Or ask me to send you a Notebook for details, if you are interested in this subject. (I don't know if it is a good practice to send a message with attachment files, otherwise I would have attached my notebook with this email.) By the way, I don't know how FullSimplify checks equality. Hope some experts may divulge this secret.