Unformatted text preview: n ∈ N such that q i = 0 for all i ≥ n . Find the cardinality of S . (5) Show that p 2 + √ 3 and 1 √ 2+ √ 3 are algebraic. Extra Credit: Show that 3 √ 2 + 3 √ 3 is irrational. Hint: First show that x = 3 √ 2 + 3 √ 3 is algebraic by constructing an explicit polynomial f ( x ) with integer coeﬃcients such that f ( x ) = 0. then prove that f ( x ) has no rational roots. 1...
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 Spring '10
 Applebaugh
 Math, Natural number, Rational number, Countable set, Algebraic number

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