https://file.aiquickdraw.com/mathbot/file/1728342260670nkg2ucxq.jpg

Let's classify each number in the table as either rational or irrational:

1. **\(-\sqrt{64}\)**: 
   \(\sqrt{64} = 8\), so \(-\sqrt{64} = -8\). Since \(-8\) is a whole number, it's a **rational** number.

2. **\(-25 \frac{1}{12}\)**:
   This represents the mixed number \(-25 \frac{1}{12}\), which can be written as \(\frac{-301}{12}\). Since it’s a ratio of two integers, it is a **rational** number.

3. **\(\sqrt{10}\)**:
   \(\sqrt{10}\) is a non-perfect square and its decimal representation is non-repeating and non-terminating. Therefore, it is an **irrational** number.

4. **\(-\frac{17}{12}\)**:
   This is already in fractional form. Since it is a ratio of two integers, it is a **rational** number.

5. **\(-5\pi\)**:
   Since \(\pi\) is an irrational number, multiplying it by any non-zero number (like \(-5\)) still results in an **irrational** number.

Here’s the completed classification:

| Expression          | Rational | Irrational |
|---------------------|----------|------------|
| \(-\sqrt{64}\)      |    ✔     |            |
| \(-25 \frac{1}{12}\)|    ✔     |            |
| \(\sqrt{10}\)       |          |     ✔      |
| \(-\frac{17}{12}\)  |    ✔     |            |
| \(-5\pi\)           |          |     ✔      |

Let me know if you need more details or have any questions!

### Related Questions:
1. How do you determine if a square root is rational or irrational?
2. What makes a number rational?
3. Can a negative number be irrational?
4. How does the multiplication of rational and irrational numbers behave?
5. Why is \(\pi\) classified as an irrational number?

### Tip:
Remember, a rational number can always be written as a fraction of two integers, while an irrational number cannot be expressed this way, and its decimal form is non-repeating and non-terminating.

Classify each number as rational or irrational.

Learn how to classify numbers like -√64, √10, and -5π as either rational or irrational. Understand the properties of rational numbers and irrational numbers, including perfect square roots and the number π.

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