Thread: composite of two field

Prove that the composite of two field Q(2^(1/2)) and Q(2^(1/3)) is the field Q(2^(1/6))

Originally Posted by apple2009

Prove that the composite of two field Q(2^(1/2)) and Q(2^(1/3)) is the field Q(2^(1/6))

Show that Q(2^(1/6)) contains both Q(2^(1/2)) and Q(2^(1/3)).

Then, show that any field containing 2^(1/2) and 2^(1/3) contains 2^(1/2) / 2^(1/3) = 2^(1/6).