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The number has a decimal representation that terminates (after 9 digits). If it terminates, the number is rational.
It is: 9/13 divided by 12/13 = 3/4 in its simplest form
No, √13 is an irrational number. Only perfect squares have whole numbers square roots, they are 1², 2³, 3², 4², ... which are 1, 4, 9, 16, ...