example

Determine whether each of the numbers in the following list is a 1. whole number, 2. integer, 3. rational number, 4. irrational number, and 5. real number. $$-7,\frac{14}{5},8,\sqrt{5},5.9,-\sqrt{64}$$ Solution: 1. The whole numbers are $0,1,2,3\dots$ The number $8$ is the only whole number given. 2. The integers are the whole numbers, their opposites, and $0$. From the given numbers, $-7$ and $8$ are integers. Also, notice that $64$ is the square of $8$ so $-\sqrt{64}=-8$. So the integers are $-7,8,-\sqrt{64}$. 3. Since all integers are rational, the numbers $-7,8,\text{and}-\sqrt{64}$ are also rational. Rational numbers also include fractions and decimals that terminate or repeat, so $\frac{14}{5}\text{and}5.9$ are rational. 4 The number $5$ is not a perfect square, so $\sqrt{5}$ is irrational. 5. All of the numbers listed are real. We'll summarize the results in a table.

Number	Whole	Integer	Rational	Irrational	Real
$-7$		$\quad\checkmark$	$\quad\checkmark$		$\quad\checkmark$
$\frac{14}{5}$			$\quad\checkmark$		$\quad\checkmark$
$8$	$\quad\checkmark$	$\quad\checkmark$	$\quad\checkmark$		$\quad\checkmark$
$\sqrt{5}$				$\quad\checkmark$	$\quad\checkmark$
$5.9$			$\quad\checkmark$		$\quad\checkmark$
$-\sqrt{64}$		$\quad\checkmark$	$\quad\checkmark$		$\quad\checkmark$