4. An integer dЄ Z\ {0} is said to be square-free if p² | d for any prime p. Let de Z\{0, 1} be square-free. Show that √√d & Q, where √d=i√√d if d <0. You may assume that if a, b and r are integers, with a, r not both zero, rlab and the greatest common divisor of a and r equal to 1, then r|b. Hint: The difficult case is d > 1. Write √√d = a/b € Q and aim for a contradiction by considering prime factors of a.

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