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SOLVED:Here is a generalization of Problem 1.8 that you may not have thought of: Lemma. Let the coefficients of the polynomial a0 a1 x a2 x^2 ⋯ am-1 x^m-1 x^m be integers. Then any real root of the polynomial is either integral or irrational. (a) Explain why the Lemma immediately implies that √(k) is irrational whenever k is not an m th power of some integer. (b) Carefully prove the Lemma. You may find it helpful to appeal to: Fact. If a prime, p, is a factor of some power of an integer, then it
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