Daniel, I think this is a case where the documentation is a bit hard to penetrate. Root is overloaded, and this type of Root uses Function objects, displayed with # and &, unfamiliar notation to many. The secrets are partly revealed in the Algebraic Numbers tutorial, the last one listed on the Root page. What somebody encountering an algebraic Root for the first time needs is the reassurance that these things are simply numbers that lack an exact representation in traditional math. It's hard to find this in the complexity of the documentation.
