Question
Which of the following rational numbers is not between 3–√ and 6–√%0D%0A3%0D%0A %0D%0A𝑎%0D%0A𝑛%0D%0A𝑑%0D%0A %0D%0A6%0D%0A ?%0D%0A%0D%0AShow your work. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A1.8%0D%0A1.8%0D%0A1 point 8%0D%0A%0D%0A4–√%0D%0A4%0D%0Asquare root of 4%0D%0A%0D%0A1.5 and 2
Answers
GPT-4o mini
To determine which of the given rational numbers is not between \( \sqrt{3} \) and \( \sqrt{6} \), let's first calculate the approximate values of \( \sqrt{3} \) and \( \sqrt{6} \):
1. **Calculating the square roots**:
- \( \sqrt{3} \approx 1.732 \)
- \( \sqrt{6} \approx 2.449 \)
So, we need to find out which of the given rational numbers lies outside the interval \( (1.732, 2.449) \).
The options are:
1. \( 1.8 \)
2. \( \sqrt{4} \) (which equals 2)
3. \( 1.5 \)
4. \( 2 \)
2. **Checking each option**:
- **\( 1.8 \)** is between \( 1.732 \) and \( 2.449 \).
- **\( \sqrt{4} = 2 \)** is also between \( 1.732 \) and \( 2.449 \).
- **\( 1.5 \)** is less than \( 1.732 \), so it is not in the interval.
- **\( 2 \)** is also in the interval, as calculated earlier.
3. **Conclusion**:
The rational number that is not between \( \sqrt{3} \) and \( \sqrt{6} \) is **\( 1.5 \)**.
Therefore, the answer is \( 1.5 \).
1. **Calculating the square roots**:
- \( \sqrt{3} \approx 1.732 \)
- \( \sqrt{6} \approx 2.449 \)
So, we need to find out which of the given rational numbers lies outside the interval \( (1.732, 2.449) \).
The options are:
1. \( 1.8 \)
2. \( \sqrt{4} \) (which equals 2)
3. \( 1.5 \)
4. \( 2 \)
2. **Checking each option**:
- **\( 1.8 \)** is between \( 1.732 \) and \( 2.449 \).
- **\( \sqrt{4} = 2 \)** is also between \( 1.732 \) and \( 2.449 \).
- **\( 1.5 \)** is less than \( 1.732 \), so it is not in the interval.
- **\( 2 \)** is also in the interval, as calculated earlier.
3. **Conclusion**:
The rational number that is not between \( \sqrt{3} \) and \( \sqrt{6} \) is **\( 1.5 \)**.
Therefore, the answer is \( 1.5 \).