Question

Determine which categories that the following numbers belong a number may be in more than one category Neutral, intriguer, and irrational
Zero, 1, -4 over -11, Square root five

Answer 1

Let's analyze each number and determine which categories they belong to: **Neutral, Intriguer,** and **Irrational**.

1. **Zero (0)**:
- Neutral: Yes, because zero is neither positive nor negative.
- Intriguer: No, not typically considered intriguing in the mathematical sense.
- Irrational: No, because zero is a rational number (it can be expressed as 0/1).

2. **One (1)**:
- Neutral: No, one is a positive number.
- Intriguer: No, one is generally considered a whole number and is not particularly intriguing.
- Irrational: No, because one is also a rational number (1 can be expressed as 1/1).

3. **-4 over -11 (-4 / -11)**:
- Neutral: No, the value is positive (4/11).
- Intriguer: No, not particularly intriguing.
- Irrational: No, because \(-4 / -11\) simplifies to \(4/11\), which is a rational number.

4. **Square root of five (√5)**:
- Neutral: No, since the value is positive (approximately 2.24).
- Intriguer: Yes, this is intriguing as it is an example of an irrational number.
- Irrational: Yes, because \(\sqrt{5}\) cannot be expressed as a simple fraction and is non-repeating and non-terminating.

### Summary:
- **Zero (0)**: Neutral
- **One (1)**: None
- **-4 over -11 (-4 / -11)**: None
- **Square root of five (√5)**: Intriguer, Irrational

So, to summarize:
- **Zero**: Neutral
- **One**: None
- **-4/-11**: None
- **Square root of five (√5)**: Intriguer, Irrational