# 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}

Then Q[x]/(x*x-2) is isomorphic to

Q(sqrt(2))={a+b*sqrt(2) | a,b are rational}

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