What is the degree of the extension [Q(√2+√3+√5):Q]?
Can you explain, what I must to do in this example?
Answer
[Q(√2+√3+√5):Q]=[Q(√2,√3,√5):Q]=[Q(√2,√3,√5):Q(√2,√3)].[Q(√2,√3):Q(√2)].[Q(√2):Q]=2.2.2=8
Q(√2+√3+√5) is a 8 degree extension over Q.And basis are 1,√2,√3,√5,√6,√10,√15,√30
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