Question

classify each number below as a rational number or an irrational number.
$-sqrt{22}$
$-sqrt{1}$
$79.overline{69}$
$33.54$
$-9pi$

Explanation:

Step1: Analyze $-\sqrt{22}$

22 is not a perfect square, so $\sqrt{22}$ is a non-repeating, non-terminating decimal. Thus, $-\sqrt{22}$ is irrational.

Step2: Analyze $-\sqrt{1}$

$\sqrt{1}=1$, so $-\sqrt{1}=-1$, which is an integer (a type of rational number).

Step3: Analyze $79.\overline{69}$

Repeating decimals can be written as a fraction of two integers, so this is rational.

Step4: Analyze $33.54$

Terminating decimals can be written as a fraction of two integers ($33.54=\frac{3354}{100}$), so this is rational.

Step5: Analyze $-9\pi$

$\pi$ is irrational, and multiplying an irrational number by a non-zero rational number ($-9$) results in an irrational number.

Answer:

Number	rational	irrational
$-\sqrt{1}$	$\bigcirc$
$79.\overline{69}$	$\bigcirc$
$33.54$	$\bigcirc$
$-9\pi$		$\bigcirc$