Answer
a) Integers: $\left\{-2,0,7 \right\}$
b) Rational Numbers: $\left\{-\dfrac{7}{3},-2,0,0.7,7,\dfrac{32}{3}\right\}$
c) Real Numbers: $\left\{-\dfrac{7}{3},-2,-\sqrt{3},0,0.7,\sqrt{12},7,\dfrac{32}{3}\right\}$
Work Step by Step
Integers are numbers from the set $\{...,-3,-2,-1,0,1,2,3,...\}$ Therefore, in the given set $
S=\left\{-\dfrac{7}{3},-2,-\sqrt{3},0,0.7,\sqrt{12},\sqrt{-8},7,\dfrac{32}{3}\right\}
$ the integers are $
\left\{-2,0,7 \right\}
$.
Rational numbers are numbers that can be expressed as the ratio of two integers. Therefore, from the given set $S$, the rational numbers are $
\left\{-\dfrac{7}{3},-2,0,0.7,7,\dfrac{32}{3}\right\}
$.
Real numbers are numbers that are not imaginary. Since $\sqrt{-8}$ is an imaginary number, then the real numbers from the given set are $
\left\{-\dfrac{7}{3},-2,-\sqrt{3},0,0.7,\sqrt{12},7,\dfrac{32}{3}\right\}
$.
