The number -√11 belongs to the following set or sets:
A. irrational numbers
C. real numbers
D. irrational numbers, real numbers
Question content area bottom
-√11
A.
irrational numbers
B.
rational numbers
C.
real numbers
D.
irrational numbers, real numbers
E.
rational numbers, real numbers
A. irrational numbers
C. real numbers
D. irrational numbers, real numbers
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.