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The image shows a table where you need to classify numbers as either rational or irrational. Let's analyze each number:

1. **\(\sqrt{64}\)**: 
   - \(\sqrt{64} = 8\), which is an integer. Integers are rational numbers.
   - **Classification**: Rational

2. **\(-85.11\)**:
   - \(-85.11\) is a terminating decimal, which can be expressed as a fraction. Therefore, it is a rational number.
   - **Classification**: Rational

3. **\(-\sqrt{7}\)**:
   - \(\sqrt{7}\) is not a perfect square, so it is an irrational number. The negative sign does not affect the irrationality.
   - **Classification**: Irrational

4. **\(54.\overline{1}\)**:
   - \(54.\overline{1}\) represents a repeating decimal (54.1111...), which can be expressed as a fraction. Repeating decimals are rational numbers.
   - **Classification**: Rational

5. **\(14\pi\)**:
   - \(\pi\) is an irrational number, and multiplying it by any non-zero rational number (such as 14) still results in an irrational number.
   - **Classification**: Irrational

**Final Table:**

| Number        | Rational | Irrational |
|---------------|----------|------------|
| \(\sqrt{64}\) | ☑        |            |
| \(-85.11\)    | ☑        |            |
| \(-\sqrt{7}\) |          | ☑          |
| \(54.\overline{1}\) | ☑   |            |
| \(14\pi\)     |          | ☑          |

Would you like further details on any of these concepts? 

Here are some related questions you might be interested in:
1. What makes a number rational or irrational?
2. How do you convert a repeating decimal into a fraction?
3. Can irrational numbers ever be written as fractions?
4. What are some other examples of irrational numbers?
5. How does the square root of a non-perfect square differ from that of a perfect square?

**Tip:** Remember, a terminating or repeating decimal is always rational!

Classify the given numbers as either rational or irrational.

Understand how to classify numbers as rational or irrational with examples like the square root of 64, -85.11, -√7, 54.1̅, and 14π. Suitable for students in Grades 6-8.

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