for an elementary proof, see http://en.wikipedia.org/wiki/Square_root_of_two#Proof_by_infinite_descent
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Justification is a written reason for why you made a statement. For example if you say a figure is a Square then you would say something like the diagonals are both congruent and perpendicular to each other.
The adjective of justification is justifiable.The adverb of justification is justifiably.
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