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.