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Math Help - dimension

  1. #1
    Senior Member Sampras's Avatar
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    dimension

    Consider  \mathbb{Q}(\sqrt{2}) . Is the dimension of  \mathbb{Q}(\sqrt{2}) equaled to  3 ? Because  \{1, \sqrt{2} \} is a basis for  \mathbb{Q}(\sqrt{2}) over  \mathbb{Q} .

    Also why does  [\mathbb{Q}(\sqrt{2}+\sqrt{3}): \mathbb{Q}] = 4 . Is it because  \text{irr}(\sqrt{2}+\sqrt{3}, \mathbb{Q}) = x^4-10x^{2}+1 ? And the degree of this polynomial is 4?
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  2. #2
    Senior Member Shanks's Avatar
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    the dimension of Q(\sqrt{2}) over Q is 2(the degree of the minimal polynomial of \sqrt{2} over Q).
    The second probelm is similar to the aboved mentioned!
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