Root objects of this type are an exact representation of algebraic numbers. Think of them as a space age replacement for bronze age radicals. As Galois proved, only a subset of algebraic numbers can be represented using radicals. Every algebraic number can be represented by a Root.
Sometimes, Mathematica can turn these into (usually more complicated) radical expressions with ToRadicals. It can always find an numerical approximation to any reasonable number of digits with N.
