Answer to Question #12703 in Abstract Algebra for Tsit Lam

Question

Find quotient ring Q[x]/(x*x-2), and find number field which it is isomorphic.

Answer 1

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}