Q: What set of numbers does the square root of 34 belong to?

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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.

Irrational

The sets of numbers that are the Square root of 5 are: 25 125

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.

The attribute that they have one square root which belongs to the set of natural numbers.

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real numbers, irrational numbers, ...

The square root of 121 is rational, an integer, and a natural number.

Root 6 is an irrational [real] number.

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.

Irrational

It belongs to many many subsets including: {sqrt(13)}, The set of square roots of integers The set of square roots of primes The set of square roots of numbers between 12 and 27 {3, -9, sqrt(13)} The set of irrational numbers The set of real numbers

The sets of numbers that are the Square root of 5 are: 25 125

odd numbers, perfect square 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.

The attribute that they have one square root which belongs to the set of natural numbers.

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.

No. The square roots of 0.25 are 0.5 AND -0.5, the second of which does not belong to the set.