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# Select the correct answer. ## Which number is an irrational number?
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Answer

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Step 1:
I'll solve this problem step by step, following the precise LaTeX formatting guidelines you specified.

Step 2:
: Understand Irrational Numbers

- Cannot be written as $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers
An irrational number is a real number that cannot be expressed as a simple fraction (ratio of two integers). Irrational numbers have decimal representations that: - Never terminate - Never repeat in a consistent pattern

Step 3:
: Examine the Given Options

Let's analyze each number to determine which is irrational:

Step 4:
\sqrt{4}

2. $$\sqrt{5}

Step 5:
\sqrt{16}

4. $$\sqrt{25}

Step 6:
: Evaluate Each Option

- $$\sqrt{25} = 5$$ (a rational number)
- \sqrt{5} (an irrational number)

Step 7:
: Identify the Irrational Number

\sqrt{5}$$ is the only irrational number in this list because it cannot be simplified to a whole number and its decimal representation is non-terminating and non-repeating.

Final Answer

\sqrt{5} is the irrational number.