Question

classify each number below as a rational number or an irrational number.
-√21
66.99
√49
49.\overline{51}
13π

Explanation:

Step1: Analyze $-\sqrt{21}$

21 is not a perfect square, so $\sqrt{21}$ is a non-terminating, non-repeating decimal. Thus, $-\sqrt{21}$ is irrational.

Step2: Analyze 66.99

66.99 is a terminating decimal, which can be written as $\frac{6699}{100}$, a ratio of integers. Thus, 66.99 is rational.

Step3: Analyze $\sqrt{49}$

$\sqrt{49}=7$, which is an integer and can be written as $\frac{7}{1}$, a ratio of integers. Thus, $\sqrt{49}$ is rational.

Step4: Analyze $49.\overline{51}$

This is a repeating decimal, which can be expressed as a ratio of integers. Thus, $49.\overline{51}$ is rational.

Step5: Analyze $13\pi$

$\pi$ is an irrational number, and multiplying an irrational number by a non-zero rational number (13) results in an irrational number. Thus, $13\pi$ is irrational.

Answer:

• $-\sqrt{21}$: irrational
• $66.99$: rational
• $\sqrt{49}$: rational
• $49.\overline{51}$: rational
• $13\pi$: irrational