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I was wondering is the field $\mathbb{Q}(\sqrt{3},\sqrt{7})$ simple extension of a field $\mathbb{Q}(\sqrt{7})$? How can we show that? Showing that the field $\mathbb{Q}(\sqrt{3},\sqrt{7})$ is simple extension of a field $\mathbb{Q}$ is easy and I understand amd know how to do that, but I really have no idea how to show this and I would really appriciate any help with this.

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Of course since $$\mathbb Q(\sqrt 3,\sqrt 7)=\mathbb Q(\sqrt 7)(\sqrt 3).$$

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  • $\begingroup$ Is that always true? $\endgroup$ – rubin May 23 '16 at 11:29

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