https://file.aiquickdraw.com/mathbot/file/1729051352116072xhet4.jpg

Let's analyze each square root in the table to determine whether the resulting number is rational or irrational.

1. **√81**:
   - √81 = 9. Since 9 is a whole number (an integer), this is a **rational** number.

2. **√15**:
   - √15 is not a perfect square, and its square root is an infinite non-repeating decimal. Hence, this is an **irrational** number.

3. **-√101**:
   - √101 is not a perfect square, and its square root is also an infinite non-repeating decimal. The negative sign does not change the fact that the square root is irrational. So, **-√101** is **irrational**.

4. **-√36**:
   - √36 = 6, which is a whole number. Therefore, **-√36 = -6** is a **rational** number.

### Final Answers:
- √81: Rational
- √15: Irrational
- -√101: Irrational
- -√36: Rational

Let me know if you'd like more details or have any questions!

### Follow-up Questions:
1. What makes a number rational versus irrational?
2. Can a negative square root ever be irrational?
3. Why is √101 irrational but √81 rational?
4. How do you classify numbers that aren't square roots—are there other ways to tell if they're rational or irrational?
5. What are some real-world applications of rational and irrational numbers?

### Tip:
A rational number can always be expressed as a fraction of two integers, while an irrational number cannot—it has a decimal expansion that goes on forever without repeating.

Determine whether each number is rational or irrational.

Learn how to determine whether numbers like √81, √15, -√101, and -√36 are rational or irrational. This problem explains key concepts such as perfect squares and the difference between rational and irrational numbers. Suitable for students in Grades 6-8.

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