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Answer to Question #12703 in Abstract Algebra for Tsit Lam

Question #12703
Find quotient ring Q[x]/(x*x-2), and find number field which it is isomorphic.
Expert's answer
x*x-2=0 => x=sqrt(2)
Then Q[x]/(x*x-2) is isomorphic to
Q(sqrt(2))={a+b*sqrt(2) | a,b are rational}

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