Question: (a) Let Q[2] = (a + b2|a, b Q}. Prove that (Q[[2], +, ) is a subring of the field (R, +, ) (Here

(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]

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a Since 0 0 2 Q2 the set Q2 is nonempty For a b2 c d2 Q2 we have a b2 c d2 a c b d5 with a c b d Q a... View full answer

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