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

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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
√(64)=8 would be S={8}.

As this subset only contains the required element (i.e.,
|S|=1), hence is the smallest possible subset.
User Bogdan Maxim
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