Choose which set or sets the following number belongs to. Be sure to account for ALL sets.
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-√17
A.
rational numbers, real numbers
B.
real numbers
C.
rational numbers
D.
irrational numbers, real numbers
E.
irrational numbers
D.
irrational numbers, real numbers
To determine which set or sets the number -√17 belongs to, we need to consider the definitions of the sets mentioned.
A rational number is a number that can be expressed as a ratio of two integers, i.e., a fraction.
An irrational number is a number that cannot be expressed as a fraction or ratio of two integers.
A real number is any number that can be located on the number line.
Given that -√17 is the square root of a non-perfect square (17), it is an irrational number. Thus, the correct answer is:
D. irrational numbers, real numbers.