Word Count : 184

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We are asked to find ([ \mathbb{Q}(\sqrt[3]{2}, \omega) : \mathbb{Q} ]), where (\omega) is a primitive cube root of unity ((\omega^3 = 1, \omega \neq 1)). First, consider the fields _______ ____ ___ _______ __________ _______ _______ ___ ___ _______ __________ _____.
_____ _____ _____ _______ _____ ______ _______ ___.
______ _______ ______ _______ _________ _________ __________ ____ ________ ______.
________ ______ __________ ______ ____ _____ ___ ____ ______ ___ _____.
_____ _____ ___ ______ _____ __________ ______ ______ _____ __________ ___.
______ ________ ____ ___ ___ ________ _________ _____ ___ _____ __________ ________.
_________ ________ __________ _______ ____ ________ _____ ____ _____ ________ _____ _______.
_________ ________ ___ _____ ___ ____ __________ _________ _____ _________ _____.
_______ _________ ___ ______ ________ ____ _____ ________ ___ ____.
___ _____ _______ ____ ___ _____ _________ ______ ___.
__________ ____ _________ __________ ________ ___ ________.
___ ___ ______ _____ __________ __________ __________ ____ _________ ___ _______.
__________ ____ ___ _________ _______ ___ _______ ________ _________ _________ _____ _________.
____ _________ ______ ______ ___ _____ __________.
______ _____ ________ _____ ___ ___ ___ ______ __________ _____.
_____.
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