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The question asks which of the following is a possible coordinate of the point shown on the number line between 2 and 5.

Here are the answer choices:
- A: \( 3\pi \)
- B: \( \sqrt{3} \)
- C: \( \sqrt{10} \)
- D: \( \sqrt[3]{10} \)

Let’s evaluate each option to determine if it falls between 2 and 5:

1. **Option A: \( 3\pi \)**
   - \( \pi \approx 3.1416 \), so \( 3\pi \approx 3 \times 3.1416 = 9.4248 \), which is greater than 5. Therefore, **this is not a possible coordinate**.

2. **Option B: \( \sqrt{3} \)**
   - \( \sqrt{3} \approx 1.732 \), which is less than 2. Therefore, **this is not a possible coordinate**.

3. **Option C: \( \sqrt{10} \)**
   - \( \sqrt{10} \approx 3.162 \), which falls between 3 and 4. Therefore, **this is a possible coordinate**.

4. **Option D: \( \sqrt[3]{10} \)**
   - \( \sqrt[3]{10} \approx 2.154 \), which is slightly greater than 2 but less than 3. Therefore, **this is not a possible coordinate** because the point on the number line is closer to 4.

Thus, the correct answer is **C: \( \sqrt{10} \)**.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore further:
1. What is the significance of irrational numbers like \( \sqrt{10} \) on a number line?
2. How do you estimate square roots to place them accurately on a number line?
3. What is the cube root of 10, and how is it approximated?
4. How does \( \pi \) relate to irrational numbers, and why is \( 3\pi \) so large?
5. How can square and cube roots be simplified or estimated for calculations?

**Tip:** When solving problems involving square roots, it helps to memorize common square root values (like \( \sqrt{2} \approx 1.414 \), \( \sqrt{3} \approx 1.732 \), etc.).

Which of the following is a possible coordinate of the point shown below? (Options: 3π, √3, √10, ³√10)

Find the possible coordinate of a point on a number line between 2 and 5. Learn to evaluate options such as square and cube roots using approximation techniques. Suitable for students in Grades 8-10.

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