Answer
a. $\sqrt{64}$
b. $0$ and $\sqrt{64}$
c. $-11, 0, \text{ and } \sqrt{64}$
d. $-11, -\frac{5}{6}, 0, 0.75, \sqrt{64}$
e. $\sqrt5$ and $\pi$
f. $-11, -\frac{5}{6}, 0, 0.75, \sqrt5, \pi, \sqrt{64}$
Work Step by Step
(a) The natural numbers are the counting numbers $1, 2, 3, ...$
Thus, the only natural number in the given set is $\sqrt{64}$ since it is equal to $8$.
(b) The whole numbers are $0, 1, 2, 3, ...$
Thus, whole numbers in the given set are $0$ and $\sqrt{64}$.
(c) The integers are $..., -3, -2, -1, 0, 1, 2, 3, ...$
Thus, the integers in the given set are $-11, 0, \sqrt{64}$.
(d) Rational numbers are numbers that can be expressed as a fraction (or a quotient of two integers, where the denominator is not zero).
Thus, the rational numbers in the given set are $-11, -\frac{5}{6}, 0, 0.75, \sqrt{64}$.
(e) Irrational numbers are numbers that cannot be expressed as a fraction (or a quotient of two integers, where the denominator is not zero).
Thus, the irrational numbers in the given set are $\sqrt5$ and $\pi$.
(f) All the numbers in the set are real numbers.
