Question
Which of the following rational numbers is not between √3 and √6
1.8
√4
1.5
2
1.8
√4
1.5
2
Answers
GPT-4o mini
To determine which of the given rational numbers is not between \(\sqrt{3}\) and \(\sqrt{6}\), we first need to find the approximate values of \(\sqrt{3}\) and \(\sqrt{6}\):
- \(\sqrt{3} \approx 1.732\)
- \(\sqrt{6} \approx 2.449\)
Now we can identify the range between \(\sqrt{3}\) and \(\sqrt{6}\):
\[1.732 < x < 2.449\]
Now we can evaluate the given options:
1. **1.8**: It is indeed between \(1.732\) and \(2.449\).
2. **\(\sqrt{4}\)**: This is equal to \(2\), which is also between \(1.732\) and \(2.449\).
3. **1.5**: This value is less than \(1.732\), so it is **not** between \(\sqrt{3}\) and \(\sqrt{6}\).
4. **2**: As previously stated, this is between \(1.732\) and \(2.449\).
Thus, the rational number that is **not** between \(\sqrt{3}\) and \(\sqrt{6}\) is **1.5**.
- \(\sqrt{3} \approx 1.732\)
- \(\sqrt{6} \approx 2.449\)
Now we can identify the range between \(\sqrt{3}\) and \(\sqrt{6}\):
\[1.732 < x < 2.449\]
Now we can evaluate the given options:
1. **1.8**: It is indeed between \(1.732\) and \(2.449\).
2. **\(\sqrt{4}\)**: This is equal to \(2\), which is also between \(1.732\) and \(2.449\).
3. **1.5**: This value is less than \(1.732\), so it is **not** between \(\sqrt{3}\) and \(\sqrt{6}\).
4. **2**: As previously stated, this is between \(1.732\) and \(2.449\).
Thus, the rational number that is **not** between \(\sqrt{3}\) and \(\sqrt{6}\) is **1.5**.