Question

(6 points) Classify each number as rational or irrational using the drop-down menu next to each number. Number Classification −15 3.67 25−−√ 2π 4.8¯¯¯ 12−−√

Answer 1

To classify each number as rational or irrational, let's review each number:

1. **−15**: This is a whole number (integer) and can be expressed as a fraction \(-15/1\). Thus, it is **rational**.

2. **3.67**: This is a terminating decimal and can also be represented as a fraction (\(367/100\)). Therefore, it is **rational**.

3. **√25**: The square root of 25 is 5, which is a whole number and can be expressed as a fraction \(5/1\). Thus, it is **rational**.

4. **2π**: \(π\) is known to be an irrational number, and multiplying it by 2 (a rational number) results in \(2π\) still being irrational. Therefore, \(2π\) is **irrational**.

5. **4.8¯¯¯**: This notation indicates a repeating decimal (4.888...), which can be expressed as a fraction. Therefore, it is **rational**.

6. **√12**: The square root of 12 simplifies to \(2\sqrt{3}\). Since \(√3\) is an irrational number, \(2\sqrt{3}\) is also irrational. Hence, \(√12\) is **irrational**.

Here is the summary:
- **−15**: Rational
- **3.67**: Rational
- **√25**: Rational
- **2π**: Irrational
- **4.8¯¯¯**: Rational
- **√12**: Irrational