Choose which set or sets the following number belongs to. Be sure to account for ALL sets.
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-√8
A.
irrational numbers
B.
rational numbers
C.
real numbers
D.
irrational numbers, real numbers
E.
rational numbers, real numbers
The number -√8 belongs to the set of irrational numbers because it is the square root of a non-perfect square, which cannot be expressed as a fraction. Therefore, the correct answer is A. irrational numbers.
It is also important to note that -√8 is a real number because it can be located on the number line. So the number belongs to the sets A. irrational numbers and C. real numbers.
However, the number -√8 is not a rational number because it cannot be expressed as a fraction or a ratio of two integers. So it does not belong to the set of rational numbers.
To determine which set or sets the number -√8 belongs to, let's analyze the given options.
A. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. The square root of 8 is not a perfect square, so -√8 is an irrational number.
B. Rational numbers: Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. Since -√8 cannot be expressed as a fraction, it is not a rational number.
C. Real numbers: Real numbers include both rational and irrational numbers. Since -√8 is an irrational number, it is also a real number.
D. Irrational numbers, real numbers: This option correctly identifies -√8 as both an irrational number and a real number.
E. Rational numbers, real numbers: This option is incorrect because -√8 is not a rational number.
Therefore, the correct answer is D. -√8 belongs to the set of irrational numbers and the set of real numbers.