https://file.aiquickdraw.com/mathbot/file/1730030153524f3nnsgum.jpg

Let's go through each question in the image to find the correct answers.

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**25. Which of the following is a possible coordinate of the point shown below?**

The point is located approximately at \( x = 5 \) on the number line.

- \( A. 3\pi \approx 9.42 \) (too far to the right)
- \( B. \sqrt{3} \approx 1.73 \) (too far to the left)
- \( C. \sqrt{10} \approx 3.16 \) (too far to the left)
- \( D. \sqrt[3]{10} \approx 2.15 \) (too far to the left)

The answer is **none of the options accurately match \( x = 5 \)**, so it's likely there is a misalignment in choices, or another interpretation may be intended.

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**26. Which number is the smallest?**

We compare:
- \( A. \frac{11}{12} \approx 0.917 \)
- \( B. \sqrt[3]{\frac{8}{9}} \approx 0.952 \)
- \( C. \frac{1}{2} = 0.5 \)
- \( D. \sqrt{\frac{1}{64}} = \frac{1}{8} = 0.125 \)

The smallest number is **D. \( \sqrt{\frac{1}{64}} \)**.

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**27. Which number is the largest?**

We compare the same values:
- \( A. \frac{11}{12} \approx 0.917 \)
- \( B. \sqrt[3]{\frac{8}{9}} \approx 0.952 \)
- \( C. \frac{1}{2} = 0.5 \)
- \( D. \sqrt{\frac{1}{64}} = 0.125 \)

The largest number is **B. \( \sqrt[3]{\frac{8}{9}} \)**.

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**28. What number lies between 0.95 and 1?**

From previous calculations:
- \( A. \frac{11}{12} \approx 0.917 \)
- \( B. \sqrt[3]{\frac{8}{9}} \approx 0.952 \)
- \( C. \frac{1}{2} = 0.5 \)
- \( D. \sqrt{\frac{1}{64}} = 0.125 \)

The number between 0.95 and 1 is **B. \( \sqrt[3]{\frac{8}{9}} \)**.

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**29. Franz says, “\( \sqrt{2} < 3 \) because \( 2 < 3 \).” What is the correct response to this?**

The reasoning is flawed because square roots don't directly relate to the original values under the root.

The correct answer is **A. It is correct that \( \sqrt{2} < 3 \), but the reason is wrong**.

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**30. Which is greater: 3.14 or \( \pi \)?**

- \( \pi \approx 3.14159 \), which is greater than 3.14.

The answer is **B. \( \pi \)**.

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Would you like further details on any question, or do you have additional questions?

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**Related Questions for Practice:**

1. What is the approximate value of \( \sqrt{2} \) and \( \sqrt{3} \)?
2. Can square roots ever be compared directly to whole numbers?
3. How do you approximate cube roots without a calculator?
4. What is the difference between rational and irrational numbers?
5. Why is \( \pi \) considered an irrational number?

**Tip:** When estimating values like square roots or cube roots, it's helpful to remember common approximations, such as \( \sqrt{2} \approx 1.414 \) and \( \sqrt{3} \approx 1.732 \).

Identify correct answers for the multiple-choice math questions shown in the image.

Find the answer key and detailed solutions for comparing square roots, cube roots, and fractions. Understand which values are the largest, smallest, and how irrational numbers like √2 relate to whole numbers. Suitable for Grades 7-9.

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