Let denote the smallest subfield of R that contains Q and
Chapter 14, Problem 26SE(choose chapter or problem)
Let \(Q(\sqrt[3]{2})\) denote the smallest subfield of \(R\) that contains \(Q\) and \(\sqrt[3]{2}\) . [That is, \(Q(\sqrt[3]{2})\)) is the subfield with the property that \(Q(\sqrt[3]{2})\) contains \(Q\) and \(\sqrt[3]{2}\) and if \(F\) is any subfield containing \(Q\) and \(\sqrt[3]{2}\) , then \(F\) contains \(Q(\sqrt[3]{2})\) .] Describe the elements of \(Q(\sqrt[3]{2})\) ).
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