https://file.aiquickdraw.com/mathbot/file/1727440653511w1qe6xf0.jpg

The problem asks to compare \(\sqrt{24}\) and 4.256 by choosing the correct number line representation.

First, let's approximate \(\sqrt{24}\):
\[
\sqrt{24} \approx 4.899
\]

Now we compare this to 4.256. Clearly, \(\sqrt{24} \approx 4.899\) is greater than 4.256.

So, on the number line, \(\sqrt{24}\) should be positioned to the right of 4.256.

### Analyzing the provided number lines:
1. **First option**: \(\sqrt{24}\) is positioned to the left of 4.256, which is incorrect.
2. **Second option**: \(\sqrt{24}\) is correctly positioned to the right of 4.256. This is the correct answer.
3. **Third option**: \(\sqrt{24}\) is positioned to the left of 4.256, which is incorrect.
4. **Fourth option**: \(\sqrt{24}\) is correctly positioned to the right of 4.256, but in this number line, \(\sqrt{24}\) is positioned incorrectly on the number line scale.

Thus, **the second number line is correct**.

Would you like further clarification or details?

Here are 5 follow-up questions related to this:
1. How do we approximate square roots manually?
2. What is the decimal approximation of other square roots like \(\sqrt{25}\)?
3. How do you compare two numbers on a number line?
4. What is the method for solving inequalities involving square roots?
5. How can square roots be simplified when solving equations?

**Tip**: Always try approximating square roots to two or three decimal places to improve accuracy in comparisons.

Choose the number line that correctly compares √24 and 4.256.

Learn how to compare square roots and decimals on a number line by approximating √24 ≈ 4.899 and comparing it with 4.256. This problem covers key concepts in number line placement and decimal approximation for middle school students.

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