Question

Determine for each number whether it is a rational or irrational number.(3 points)
Rational Irrational
π2
𝜋
2


3–√
3


−25−−√

Answer 1

u sure

Answer 2

To determine whether each number is rational or irrational, we can use the definitions:

- A rational number can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).
- An irrational number cannot be expressed as a simple fraction; it has a non-repeating and non-terminating decimal expansion.

Let's analyze each number one by one:

1. **\( \pi^2 \)**:
- \( \pi \) is an irrational number; its square, \( \pi^2 \), is also irrational.
- **Classification**: **Irrational**

2. **\( \pi \)**:
- \( \pi \) itself is a well-known irrational number.
- **Classification**: **Irrational**

3. **\( \sqrt{3} \)**:
- \( 3 \) is not a perfect square, and therefore \( \sqrt{3} \) is an irrational number.
- **Classification**: **Irrational**

4. **\(-\sqrt{25}\)**:
- \( \sqrt{25} = 5 \), which is rational, and thus \(-\sqrt{25} = -5\) is also rational.
- **Classification**: **Rational**

### Summary:
| Number | Classification |
|----------------|----------------|
| \( \pi^2 \) | Irrational |
| \( \pi \) | Irrational |
| \( \sqrt{3} \) | Irrational |
| \(-\sqrt{25}\) | Rational |

Answer 3

Yes, let's summarize the classifications again to ensure clarity and correctness:

1. **\( \pi^2 \)**:
- **Classification**: **Irrational**. (Since \( \pi \) is irrational, \( \pi^2 \) is also irrational).

2. **\( \pi \)**:
- **Classification**: **Irrational**. (Known fact that \( \pi \) is an irrational number).

3. **\( \sqrt{3} \)**:
- **Classification**: **Irrational**. (Since 3 is not a perfect square, \( \sqrt{3} \) is irrational).

4. **\(-\sqrt{25}\)**:
- \( \sqrt{25} = 5 \), so \(-\sqrt{25} = -5\).
- **Classification**: **Rational**. (Since \(-5\) can be expressed as \(-\frac{5}{1}\), it is a rational number).

### Final Summary:
| Number | Classification |
|----------------|----------------|
| \( \pi^2 \) | Irrational |
| \( \pi \) | Irrational |
| \( \sqrt{3} \) | Irrational |
| \(-\sqrt{25}\) | Rational |

I appreciate your patience, and I stand by these classifications based on the definitions of rational and irrational numbers. If you have any further questions or need more clarifications, feel free to ask!