Asked by yayy
which of the following are irrational numbers
pi
62
square root of 47
square root of 26
pi
62
square root of 47
square root of 26
Answers
Answered by
GPT-4o mini
Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have non-repeating, non-terminating decimal expansions.
Let's analyze each of the given numbers:
1. **π (pi)**: This is an irrational number.
2. **62**: This is a whole number (integer) and can be expressed as a fraction (62/1), so it is not irrational.
3. **√47**: This is an irrational number because 47 is not a perfect square.
4. **√26**: This is also an irrational number because 26 is not a perfect square.
In conclusion, the irrational numbers from your list are:
- π
- √47
- √26
Let's analyze each of the given numbers:
1. **π (pi)**: This is an irrational number.
2. **62**: This is a whole number (integer) and can be expressed as a fraction (62/1), so it is not irrational.
3. **√47**: This is an irrational number because 47 is not a perfect square.
4. **√26**: This is also an irrational number because 26 is not a perfect square.
In conclusion, the irrational numbers from your list are:
- π
- √47
- √26
Answered by
GPT-4o mini
Let's evaluate each of the given numbers to determine which are irrational:
1. **√48**: This can be simplified as √(16 * 3) = 4√3. Since √3 is an irrational number, √48 is also irrational.
2. **3 and 2/22**: This can be expressed as \(3 + \frac{2}{22} = 3 + \frac{1}{11} = \frac{34}{11}\), which is a rational number because it can be expressed as a fraction of two integers.
3. **0**: This is a rational number since it can be expressed as 0/1.
4. **-7**: This is also a rational number because it can be expressed as a fraction (-7/1).
In conclusion, from your list, the only irrational number is:
- √48
All the other numbers (3 and 2/22, 0, -7) are rational.
1. **√48**: This can be simplified as √(16 * 3) = 4√3. Since √3 is an irrational number, √48 is also irrational.
2. **3 and 2/22**: This can be expressed as \(3 + \frac{2}{22} = 3 + \frac{1}{11} = \frac{34}{11}\), which is a rational number because it can be expressed as a fraction of two integers.
3. **0**: This is a rational number since it can be expressed as 0/1.
4. **-7**: This is also a rational number because it can be expressed as a fraction (-7/1).
In conclusion, from your list, the only irrational number is:
- √48
All the other numbers (3 and 2/22, 0, -7) are rational.
Answered by
GPT-4o mini
Let's analyze each of the given numbers:
1. **√9**: This equals 3, which is a rational number because it can be expressed as a fraction (3/1).
2. **-716**: This is a whole number (integer) and can be expressed as a fraction (-716/1), so it is a rational number.
3. **300.666...**: The decimal representation 300.666... can also be written as \(300 + \frac{2}{3}\) (since 0.666... is equal to \(\frac{2}{3}\)). This can be expressed as a fraction, making it a rational number.
In conclusion, none of the numbers listed are irrational. All are rational:
- √9 = 3 (rational)
- -716 (rational)
- 300.666... (rational)
1. **√9**: This equals 3, which is a rational number because it can be expressed as a fraction (3/1).
2. **-716**: This is a whole number (integer) and can be expressed as a fraction (-716/1), so it is a rational number.
3. **300.666...**: The decimal representation 300.666... can also be written as \(300 + \frac{2}{3}\) (since 0.666... is equal to \(\frac{2}{3}\)). This can be expressed as a fraction, making it a rational number.
In conclusion, none of the numbers listed are irrational. All are rational:
- √9 = 3 (rational)
- -716 (rational)
- 300.666... (rational)
Answered by
GPT-4o mini
Let's evaluate each of the given numbers to determine which are rational or irrational:
1. **94**: This is a whole number (integer) and can be expressed as a fraction (94/1), so it is a rational number.
2. **√194**: The square root of 194 is not a perfect square—it cannot be expressed as a fraction of two integers. Therefore, √194 is an **irrational number**.
3. **π (pi)**: This number is well-known to be an **irrational number** as it cannot be expressed as a fraction of two integers and has a non-terminating, non-repeating decimal expansion.
4. **341**: This is also a whole number (integer) and can be expressed as a fraction (341/1), so it is a rational number.
In conclusion, the irrational numbers from your list are:
- **√194**
- **π**
The rational numbers are:
- **94**
- **341**
1. **94**: This is a whole number (integer) and can be expressed as a fraction (94/1), so it is a rational number.
2. **√194**: The square root of 194 is not a perfect square—it cannot be expressed as a fraction of two integers. Therefore, √194 is an **irrational number**.
3. **π (pi)**: This number is well-known to be an **irrational number** as it cannot be expressed as a fraction of two integers and has a non-terminating, non-repeating decimal expansion.
4. **341**: This is also a whole number (integer) and can be expressed as a fraction (341/1), so it is a rational number.
In conclusion, the irrational numbers from your list are:
- **√194**
- **π**
The rational numbers are:
- **94**
- **341**