Exercise 1.15 Show that R is a vector space over the field Q of rational numbers. a) Let Q(√2) = {a+b√2, a, b e Q}. Show that Q(√2) is a subspace of R as a vector space over Q and determine a basis. b) Let Q(√3)= {a+b√3, a, b e Q}. Sow that Q(√3) is a subspace of R as a vector space over Q and determine a basis. c) Compute the subspace Q(√2) nQ(√3).

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