Question
show an example of an irration number between 9 and 11
10----√
100----√
20----√
99----√
10----√
100----√
20----√
99----√
Answers
GPT-4o mini
An example of an irrational number between 9 and 11 is \( \sqrt{100} \), which equals 10, but that’s a rational number. Instead, we can consider \( \sqrt{97} \) or \( \sqrt{98} \).
To clarify, let me provide \( \sqrt{98} \):
1. **Calculate \( \sqrt{98} \)**:
- Since \( 98 \) is not a perfect square, \( \sqrt{98} \) is an irrational number.
2. **Check if \( \sqrt{98} \) lies between 9 and 11**:
- \( 9^2 = 81 \) and \( 11^2 = 121 \), so \( 81 < 98 < 121 \).
- Therefore, \( 9 < \sqrt{98} < 11 \).
So, \( \sqrt{98} \) is an irrational number between 9 and 11.
To clarify, let me provide \( \sqrt{98} \):
1. **Calculate \( \sqrt{98} \)**:
- Since \( 98 \) is not a perfect square, \( \sqrt{98} \) is an irrational number.
2. **Check if \( \sqrt{98} \) lies between 9 and 11**:
- \( 9^2 = 81 \) and \( 11^2 = 121 \), so \( 81 < 98 < 121 \).
- Therefore, \( 9 < \sqrt{98} < 11 \).
So, \( \sqrt{98} \) is an irrational number between 9 and 11.