## Thinking Mathematically (6th Edition)

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. $-11, -\frac{5}{6}, 0, 0.75, \sqrt5, \pi, \sqrt{64}$
(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.