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Let $\alpha=\sqrt{2+\sqrt{3}}$.

Let $L=\mathbb{Q}(\alpha)$.

Determine $Gal(L/\mathbb{Q})$

Thanks for your help.

moona
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  • Your attempts? Have you found the minimal polynomial of $\alpha$? And the conjugates of $\alpha$? Did you realize that $L$ is a biquadratic extension of $\mathbb{Q}$? – Jack D'Aurizio Nov 14 '17 at 19:43
  • The same question was a few hours ago. I gave already an answer with links - see here. Please do not repost the same question twice! – Dietrich Burde Nov 14 '17 at 19:43
  • but here i want to determine the Galoi groupe of the quotient – moona Nov 14 '17 at 19:47
  • This is not true. You wrote:"Determine $Gal(L/\mathbb{Q})$", i.e., the Galois group of the extension $L/\mathbb{Q}$ (this is not a quotient but rather a field extension). – Dietrich Burde Nov 14 '17 at 19:48

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