How would one show that $[\mathbb{Q}(\sqrt2, \sqrt3,...,\sqrt{p_n},...)]=\infty$? I know that we want to show there is no finite basis over the rationals, but I'm not sure how one would determine that such a basis does not exist.
How would one show that $[\mathbb{Q}(\sqrt2, \sqrt3,...,\sqrt{p_n},...)]=\infty$? I know that we want to show there is no finite basis over the rationals, but I'm not sure how one would determine that such a basis does not exist.
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