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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