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- Jun 22, 2012

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7. Prove that [TEX] \mathbb{Q} ( \sqrt{2} + \sqrt{3} ) = \mathbb{Q} ( \sqrt{2} , \sqrt{3} )[/TEX].

Conclude that [TEX] [\mathbb{Q} ( \sqrt{2} + \sqrt{3} ) \ : \ \mathbb{Q} ] = 4 [/TEX].

Find an irreducible polynomial satisfied by [TEX] \sqrt{2} + \sqrt{3} [/TEX]

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I am somewhat overwhelmed by this problem ... can someone advise me on an approach ... and, indeed, get me started?

Peter

[This has also been posted on MHF]