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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.
The sets of numbers that are the Square root of 5 are: 25 125
Yes, the square root of negative 121 is undefined in the set of real numbers. However, in the set of complex numbers, the square root of negative 121 is equal to 11i, where i is the imaginary unit.
The attribute that they have one square root which belongs to the set of natural numbers.
2 does belong to the set of imaginary numbers. Any real number is also imaginary. Imaginary numbers are the set of all numbers that can be expressed as a +b*i where "i" is the square root of negative one and "a" and "b" are both real numbers.