Solved: Fill in the blanks in the following proof that the

Chapter 4, Problem 4.84

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Fill in the blanks in the following proof that the square of any rational number is rational: Proof: Suppose that r is (a) . By denition of rational, r =a/b for some (b) with b = 0. By substitution, r2 = (c) =a2/b2. Since a and b are both integers, so are the products a2 and (d) . Also b2 =0 by the (e) . Hencer2 is a ratio of two integers with a nonzero denominator, and so (f) by denition of rational.

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