Asked by Gelo
Which are Rational or irrational numbers?
Pi,
-√9,
0,
3√25,
5/4,
-√2/2
Pi,
-√9,
0,
3√25,
5/4,
-√2/2
Answers
Answered by
GPT-4o mini
Let's classify the given numbers as rational or irrational:
1. **π (Pi)**: This is an irrational number because it cannot be expressed as a fraction of two integers.
2. **-√9**: The square root of 9 is 3, so -√9 = -3, which is a rational number (it can be expressed as -3/1).
3. **0**: This is a rational number (it can be expressed as 0/1).
4. **3√25**: The square root of 25 is 5, so 3√25 = 3 * 5 = 15, which is a rational number (15 can be expressed as 15/1).
5. **5/4**: This is a rational number because it is a fraction of two integers.
6. **-√2/2**: The square root of 2 is an irrational number, and when divided by 2, it remains irrational. Therefore, -√2/2 is also an irrational number.
In summary:
- **Irrational numbers**: π, -√2/2
- **Rational numbers**: -√9, 0, 3√25, 5/4
1. **π (Pi)**: This is an irrational number because it cannot be expressed as a fraction of two integers.
2. **-√9**: The square root of 9 is 3, so -√9 = -3, which is a rational number (it can be expressed as -3/1).
3. **0**: This is a rational number (it can be expressed as 0/1).
4. **3√25**: The square root of 25 is 5, so 3√25 = 3 * 5 = 15, which is a rational number (15 can be expressed as 15/1).
5. **5/4**: This is a rational number because it is a fraction of two integers.
6. **-√2/2**: The square root of 2 is an irrational number, and when divided by 2, it remains irrational. Therefore, -√2/2 is also an irrational number.
In summary:
- **Irrational numbers**: π, -√2/2
- **Rational numbers**: -√9, 0, 3√25, 5/4