How to get an answer as a Root object?

*To*: mathgroup at smc.vnet.net*Subject*: [mg57137] How to get an answer as a Root object?*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Tue, 17 May 2005 01:20:00 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

This question must have an obvious answer! A certain expression, given below my signature, involves nothing worse than some nested square roots. It equals 0 for a value of the variable s near 2.707, easily approximated using FindRoot. However, I would like to get that value expressed precisely as a Root object. Trying to use Solve or Reduce to do that, Mathematica seems to take "forever". Of course, I could do this by hand; in the days before CASs -- before I got spoiled by them! -- I wouldn't have hesitated to do so. But surely there must be an easy way to get Mathematica to give that value as a Root object. How? David Cantrell (-1 + Sqrt[2] - Sqrt[(1 + 2*Sqrt[2] - s)*(-1 + s)] + s)*(-1 - Sqrt[2] + Sqrt[2]*s - Sqrt[-1 - 2*Sqrt[2] + 2*(2 + Sqrt[2] - s)*s]) - (-1 - Sqrt[2] + Sqrt[2]*s + Sqrt[-1 - 2*Sqrt[2] + 2*(2 + Sqrt[2] - s)*s])* (-2 - 2*Sqrt[2] + 2*s + 2*Sqrt[1 - (1/4)*(-1 - Sqrt[2] + Sqrt[(1 + 2*Sqrt[2] - s)*(-1 + s)] + s)^2])

**Follow-Ups**:**Re: How to get an answer as a Root object?***From:*Daniel Lichtblau <danl@wolfram.com>