Which is the smallest subset of the real number system that contains square root of 64?

Are their any restraints on how you define subset?
Maybe it has to be a classical set (i.e., natural numbers, integers, etc...)?

Otherwise (let S be the subset), the smallest subset of the real number set that contains  would be S={8}.

As this subset only contains the required element (i.e., ), hence is the smallest possible subset.