Question
Between which pair of rational numbers on a number line does V38
lie? (1 point)
Between 6.3 and 6.5
Between 19 and 19.2
• Between 18.9 and 19.1
lie? (1 point)
Between 6.3 and 6.5
Between 19 and 19.2
• Between 18.9 and 19.1
Answers
GPT-4o mini
To find between which pair of rational numbers \(\sqrt{38}\) (V38) lies, we first need to calculate its approximate value.
Calculating \(\sqrt{38}\):
The perfect squares around 38 are \(36\) (which is \(6^2\)) and \(49\) (which is \(7^2\)). This means:
\[ 6 < \sqrt{38} < 7 \]
For a more precise approximation, we can use a calculator or estimate further.
Calculating directly, we get:
\[
\sqrt{38} \approx 6.164
\]
Now, we check where this value lies among the given ranges:
1. **Between 6.3 and 6.5**: No, because \(6.164\) is less than \(6.3\).
2. **Between 19 and 19.2**: No, because \(6.164\) is far less than \(19\).
3. **Between 18.9 and 19.1**: No, because \(6.164\) is also far less than \(18.9\).
Since \(6.164\) does not fit in any of the given ranges, it strictly lies between \(6\) and \(7\).
Therefore, it seems that none of the provided answer pairs correctly contain \(\sqrt{38}\).
Calculating \(\sqrt{38}\):
The perfect squares around 38 are \(36\) (which is \(6^2\)) and \(49\) (which is \(7^2\)). This means:
\[ 6 < \sqrt{38} < 7 \]
For a more precise approximation, we can use a calculator or estimate further.
Calculating directly, we get:
\[
\sqrt{38} \approx 6.164
\]
Now, we check where this value lies among the given ranges:
1. **Between 6.3 and 6.5**: No, because \(6.164\) is less than \(6.3\).
2. **Between 19 and 19.2**: No, because \(6.164\) is far less than \(19\).
3. **Between 18.9 and 19.1**: No, because \(6.164\) is also far less than \(18.9\).
Since \(6.164\) does not fit in any of the given ranges, it strictly lies between \(6\) and \(7\).
Therefore, it seems that none of the provided answer pairs correctly contain \(\sqrt{38}\).