https://file.aiquickdraw.com/mathbot/file/17261877123709y1810zs.jpg

The problem in the image is asking:

**"To which set(s) of numbers does \( \sqrt[3]{100} \) belong? Select all that apply."**

Let's first evaluate and categorize \( \sqrt[3]{100} \) (the cube root of 100):

1. **\( \sqrt[3]{100} \)** is approximately equal to **4.64**, which is a non-integer value.
2. **Classification**:
   - **Whole Numbers**: Whole numbers are non-negative integers (0, 1, 2, 3, ...). Since \( \sqrt[3]{100} \) is not an integer, it is **not a whole number**.
   - **Natural Numbers**: Natural numbers are positive integers (1, 2, 3, ...). Since \( \sqrt[3]{100} \) is not a positive integer, it is **not a natural number**.
   - **Integers**: Integers are positive and negative whole numbers (..., -2, -1, 0, 1, 2, ...). Since \( \sqrt[3]{100} \) is not a whole number, it is **not an integer**.
   - **Rational Numbers**: Rational numbers are numbers that can be expressed as a fraction of two integers. Since \( \sqrt[3]{100} \) is a real number that can be expressed as a non-terminating decimal, it is a **rational number**.
   - **Irrational Numbers**: Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. Since \( \sqrt[3]{100} \) can be written as a fraction, it is **not irrational**.

### Correct sets:
- **Rational**.

Would you like any additional details or explanations?

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Here are 5 follow-up questions that might interest you:
1. How do we determine if a number is rational or irrational?
2. What is the difference between whole numbers and integers?
3. How is the cube root of a number calculated manually?
4. Can the cube root of any number ever be an integer?
5. How do decimal approximations affect classifying numbers?

**Tip**: A rational number is any number that can be expressed as the ratio of two integers, even if its decimal form is repeating or terminating.

To which set(s) of numbers does the cube root of 100 belong? Select all that apply.

Understand which sets the cube root of 100 belongs to with this detailed explanation. Learn the classification of numbers into natural, whole, integers, rational, and irrational categories. This problem is suitable for students in Grades 7-9.

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