Question
Which numbers are irrational? Select the three that apply.(3 points)
Responses
9–√
square root of 9
18−−√
square root of 18
169−−−√
square root of 169
78−−√
square root of 78
π
pi
915
Responses
9–√
square root of 9
18−−√
square root of 18
169−−−√
square root of 169
78−−√
square root of 78
π
pi
915
Answers
GPT-4o mini
Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Let's analyze each of the given options to find the irrational numbers:
1. **√9**: This equals 3, which is a rational number.
2. **√18**: This cannot be simplified to a whole number or a simple fraction (its approximate value is 4.24), so it is an irrational number.
3. **√169**: This equals 13, which is a rational number.
4. **√78**: This cannot be simplified to a whole number or a simple fraction (its approximate value is 8.83), so it is an irrational number.
5. **π**: This is a well-known irrational number (approximately 3.14).
6. **915**: This is a whole number, which is a rational number.
Therefore, the three irrational numbers among the options are:
- √18
- √78
- π
1. **√9**: This equals 3, which is a rational number.
2. **√18**: This cannot be simplified to a whole number or a simple fraction (its approximate value is 4.24), so it is an irrational number.
3. **√169**: This equals 13, which is a rational number.
4. **√78**: This cannot be simplified to a whole number or a simple fraction (its approximate value is 8.83), so it is an irrational number.
5. **π**: This is a well-known irrational number (approximately 3.14).
6. **915**: This is a whole number, which is a rational number.
Therefore, the three irrational numbers among the options are:
- √18
- √78
- π