just out of curiosity, is there a point of de-nesting if it leads to more square roots? bob baillie --- Warut Roonguthai wrote:
Another example, sqrt(3+sqrt(5+2*sqrt(3))) = 1/2 + sqrt(3)/2 + sqrt((4-sqrt(3))/2).
If (a^2-b)^2-c is a perfect square, then sqrt(a+sqrt(b+sqrt(c))) can be (partially) denested.
Warut
On Sat, Nov 24, 2012 at 4:22 PM, Bill Gosper <billgosper@gmail.com> wrote:
It's clear that √(a+√(b+√c)) can't completely denest unless √(b+√c) does. Failing that, I'd've expected nothing better than √(b+√c) + √d + √e + ..., i.e., the √(b+√c) would act atomically, like √integer. But
Sqrt[1/2 - Sqrt[-2 + Sqrt[5]]] == 1/2 Sqrt[-1 + Sqrt[5]] + 1/4 (Sqrt[2] - Sqrt[10]) --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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