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The real number system is a number system using the rational and irrational numbers.
A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.
Real numbers are madeup of rational and irrational numbers
The set of all rational numbers.If the set contains all of them then no other set can contain any more rational numbers.
Natural Number, Integers, Rational Numbers, Irrational Numbers