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Let $p_{1}$ $\neq$ $p_{2}$ $\neq$ $p_{3}$ prime numbers. Compute the grades over $\mathbb{Q}$ of the extension fields $\mathbb{Q} ( \sqrt{p_{1}}, \sqrt{p_{2}})$ and $\mathbb{Q} ( \sqrt{p_{2}}, \sqrt{p_{2}}, \sqrt{p_{3}})$.

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marked as duplicate by Dietrich Burde, egreg, Shaun, user147263, Davide Giraudo Apr 21 '15 at 15:33

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    $\begingroup$ ...please ...?! What are your ideas, insights, self work, etc.? $\endgroup$ – Timbuc Apr 21 '15 at 14:40
  • $\begingroup$ Amusingly, an extension field doesn't have a grade, but a degree. Your homework, on the other hand, will indeed have a grade... $\endgroup$ – A.P. Apr 21 '15 at 14:43