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No best answer has yet been selected by moloi. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.The traditional way of doing this is to assume that root(2) IS rational and then show that this leads to a contradiction.
see here for some proofs
http://en.wikipedia.org/wiki/Square_root_of_2
see here for some proofs
http://en.wikipedia.org/wiki/Square_root_of_2