Question

classify each number as rational or irrational. explain how you classified each number.
-81,572 √11 5.636336333… √16
rational irrational

Explanation:

Step1: Recall definitions

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$. This includes integers, terminating decimals, repeating decimals, and perfect square roots. An irrational number is a non - repeating, non - terminating decimal and non - perfect square roots.

Step2: Classify - 81,572

• 81,572 is an integer. Integers can be written as $\frac{- 81572}{1}$, so it is a rational number.

Step3: Classify $\sqrt{11}$

11 is not a perfect square (since $3^2 = 9$ and $4^2=16$), so $\sqrt{11}$ is a non - repeating, non - terminating decimal. Thus, $\sqrt{11}$ is an irrational number.

Step4: Classify 5.636336333...

The decimal 5.636336333... is a non - repeating, non - terminating decimal (the pattern of digits does not repeat in a fixed cycle). So it is an irrational number.

Step5: Classify $\sqrt{16}$

We know that $\sqrt{16}=4$, and 4 can be written as $\frac{4}{1}$. So $\sqrt{16}$ is a rational number.

Answer:

Rational: - 81,572, $\sqrt{16}$
Irrational: $\sqrt{11}$, 5.636336333...