Choose which set or sets the following number belongs to. Be sure to account for ALL sets.
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-√11
A.
irrational numbers
B.
rational numbers
C.
real numbers
D.
irrational numbers, real numbers
E.
rational numbers, real numbers
The number -√11 belongs to the following set or sets:
A. irrational numbers
C. real numbers
D. irrational numbers, real numbers
To determine which set or sets the number -√11 belongs to, let's analyze each option:
A. Irrational numbers: An irrational number is a number that cannot be expressed as a fraction. Since -√11 cannot be expressed as a fraction (or a terminating or repeating decimal), it is indeed an irrational number.
B. Rational numbers: A rational number is a number that can be expressed as a fraction. Since -√11 cannot be expressed as a fraction, it is not a rational number.
C. Real numbers: Real numbers include both rational and irrational numbers. Since -√11 falls under the category of irrational numbers, it is also included in the set of real numbers.
Based on the analysis, the correct answer would be:
D. Irrational numbers, real numbers
Note that the number -√11 does not belong to the set of rational numbers, so E (rational numbers, real numbers) is incorrect.