Talk:Nested radical

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The page Exact_trigonometric_constants has a bit of a longer discussion on this, but I don't quite get the math.

I don't understand how the quadradic formula can be used to solve for d and e. I've looked everywhere on the Internet and nowhere dose it actually show the deverivation of the formula for denesting radicals.

Quick explanation: if we assume that there exist rational d and e such that \sqrt{a+b\sqrt{c}}=\sqrt{d}+\sqrt{e}, then by squaring we get a+b\sqrt{c}=d+e+2\sqrt{de} as the article says. Then, we equate the rational and irrational parts, giving us a=d+e\, and b\sqrt{c}=2\sqrt{de}\rightarrow de=b^2c/2 and you can rearrange the last two to give quadratic formulae for d and e in terms of a, b and c. Of course, it may turn out that your quadratics don't resolve into nice rational expressions, in which case you're screwed. Confusing Manifestation 01:59, 6 June 2007 (UTC)