(a) Let Q[√2] = (a + b√2|a, b ∈ Q}. Prove that
(Q[[√2], +, •) is a subring of the field (R, +, •)• (Here the binary operations in R and Q[√2] are those of ordinary addition and multiplication of real numbers.)
(b) Prove that Q[√2] is a field and that Q[x] /(x2- 2) is isomorphic to Q[√2]