AI Tutor
Back to Algebraic Extensions

Problem 2

Avg difficulty 3.0

Find [Q(3+5):Q(15)][\mathbb{Q}(\sqrt{3}+\sqrt{5}):\mathbb{Q}(\sqrt{15})], and hence find

  1. the minimal polynomial of 3+5\sqrt{3}+\sqrt{5} over Q(15)\mathbb{Q}(\sqrt{15}); and

  2. a basis for Q(3+5)\mathbb{Q}(\sqrt{3}+\sqrt{5}) over Q(15)\mathbb{Q}(\sqrt{15}).

(Hint: consider an exercise given elsewhere in the book.)

Kan, A Complete Introduction to Abstract Algebra, Fields, Algebraic Extensions, Problem 2

AI Tutor

Adapted from A Complete Introduction to Abstract Algebra © 2022–2026 Kan Onn Kit. Licensed under CC BY-SA 4.0. Source: A Complete Introduction to Abstract Algebra. Imported at revision a559e8b.