Asked by hola
Which number is irrational?
Responses
8√
square root of 8
0.46
0.46
100√3
fraction numerator square root of 100 end numerator over denominator 3 end fraction
0.8¯
Responses
8√
square root of 8
0.46
0.46
100√3
fraction numerator square root of 100 end numerator over denominator 3 end fraction
0.8¯
Answers
Answered by
GPT-4o mini
To determine which of the provided numbers is irrational, let's evaluate each one:
1. **8√**: This appears to be "8 times the square root of some number." Since the square root of a non-perfect square is irrational (like \( \sqrt{2}, \sqrt{3}, \) etc.), but if it's interpreted as \( 8\sqrt{n} \) with \( n \) being a perfect square (like \( 4 \) or \( 16 \)), it could be rational. Without that information, we cannot classify it reliably.
2. **Square root of 8**: The square root of 8 can be simplified to \( 2\sqrt{2} \). Since \( \sqrt{2} \) is irrational, \( \sqrt{8} \) is also irrational.
3. **0.46**: This is a terminating decimal number, which is rational. It can be expressed as a fraction (46/100).
4. **100√3**: This is 100 times the square root of 3. Since \( \sqrt{3} \) is irrational, multiplying it by 100 keeps it irrational.
5. **0.8¯**: This represents a repeating decimal, specifically \( 0.888...\), which can be expressed as \( 8/9 \), making it a rational number.
Considering these evaluations, the numbers that are irrational are:
- **Square root of 8**
- **100√3**
However, since the original question asks for "which number is irrational?" and does not allow multiple choices, the most straightforward answer indicating irrationality is:
**Square root of 8** (as this is recognized clearly as irrational without needing to consider more complexities).
1. **8√**: This appears to be "8 times the square root of some number." Since the square root of a non-perfect square is irrational (like \( \sqrt{2}, \sqrt{3}, \) etc.), but if it's interpreted as \( 8\sqrt{n} \) with \( n \) being a perfect square (like \( 4 \) or \( 16 \)), it could be rational. Without that information, we cannot classify it reliably.
2. **Square root of 8**: The square root of 8 can be simplified to \( 2\sqrt{2} \). Since \( \sqrt{2} \) is irrational, \( \sqrt{8} \) is also irrational.
3. **0.46**: This is a terminating decimal number, which is rational. It can be expressed as a fraction (46/100).
4. **100√3**: This is 100 times the square root of 3. Since \( \sqrt{3} \) is irrational, multiplying it by 100 keeps it irrational.
5. **0.8¯**: This represents a repeating decimal, specifically \( 0.888...\), which can be expressed as \( 8/9 \), making it a rational number.
Considering these evaluations, the numbers that are irrational are:
- **Square root of 8**
- **100√3**
However, since the original question asks for "which number is irrational?" and does not allow multiple choices, the most straightforward answer indicating irrationality is:
**Square root of 8** (as this is recognized clearly as irrational without needing to consider more complexities).