QuestionDetermine if the number $\sqrt{99}$ is rational or irrational. Choose: rational or irrational.

Studdy Solution

STEP 1

Assumptions1. A rational number is a number that can be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq0$ . . An irrational number is a number that cannot be expressed as a simple fraction. It's decimal goes on forever without repeating.
3. The number we are examining is $\sqrt{99}$ .

STEP 2

First, we need to calculate the square root of99.
$\sqrt{99}$

STEP 3

The square root of99 is a non-terminating, non-repeating decimal number.
$\sqrt{99} \approx9.94987437107$

STEP 4

Since the decimal representation of $\sqrt{99}$ is non-terminating and non-repeating, it cannot be expressed as a fraction of two integers.

STEP 5

Therefore, $\sqrt{99}$ is an irrational number.
The number $\sqrt{99}$ is irrational.

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