https://file.aiquickdraw.com/mathbot/file/17268624431723sikozj8.jpg

Let’s go over the comparisons in the image to determine which are true.

1. **\( \sqrt{7} > 3.3 \)**  
   - \( \sqrt{7} \approx 2.645751 \), and \( 3.3 \) is greater than this.  
   - **This is false**.

2. **\( 3\pi > 8 \)**  
   - \( 3\pi \approx 9.424777 \), and \( 9.42 > 8 \).  
   - **This is true**.

3. **\( \sqrt{2} < \frac{7}{10} \)**  
   - \( \sqrt{2} \approx 1.414 \), and \( \frac{7}{10} = 0.7 \).  
   - Since \( 1.414 > 0.7 \), **this is false**.

4. **\( \frac{5}{4} < 2 \)**  
   - \( \frac{5}{4} = 1.25 \), and \( 1.25 < 2 \).  
   - **This is true**.

5. **\( \sqrt{101} < 9.8 \)**  
   - \( \sqrt{101} \approx 10.05 \), and \( 10.05 > 9.8 \).  
   - **This is false**.

### Correct Comparisons:
- \( 3\pi > 8 \)
- \( \frac{5}{4} < 2 \)

Would you like further details on any specific comparison?

Here are some related questions to explore:
1. How do you approximate square roots without a calculator?
2. What is the process for comparing irrational and rational numbers?
3. How can you use inequalities to solve equations with square roots?
4. What are some common irrational numbers and their approximations?
5. How do you estimate \( \pi \)-related values like \( 3\pi \)?

**Tip:** When approximating square roots, use nearby perfect squares as reference points for better accuracy.

Select all the comparisons that are true.

Learn how to compare irrational numbers such as square roots and multiples of Pi. This problem includes key concepts like approximating square roots, using inequalities, and rational versus irrational number comparisons. Suitable for Grades 8-10.

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