galpis theoream algebra part 1 2 3 4 Question II:1. Show that Q(√2, √5) = Q(√2 + √5).2. Find [Q(√2,√5): Q] and describe the elements of Q(√2, √5) over Q.3. Deduce √2 + √5 is algebraic over Q.4. Find Gal(Q(√2,√5)/Q).5. Is Gal(Q(√2, √5)/Q) cyclic? Abelian?Justify.6. Let H be a subgroup of Gal(E/Q). find EH.7. Draw the lattice of subgroups of Gal (E/Q). Deduce all subfields of Q(√2, √5).8. Deduce | Gal(Q(√10/Q)|.

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Advanced Engineering Mathematics

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Question II: 1. Show that Q(√2, √5) = Q(√2+ √5). 2. Find [Q(√2, √5): Q] and describe the elements of Q(√2, √5) over Q. 3. Deduce √2 + √5 is algebraic over Q.