Question
Walter is using the iterative process to determine that 13−−√
is between 3.61 and 3.62. Analyze Walter's estimation. Is he correct? If not, what mistake did he make?(1 point)
Responses
Yes, Walter is correct.
Yes, Walter is correct.
No, 3.612
is less than 13.
No, 3 point 6 1 squared is less than 13.
No, both 3.612
and 3.622
are less than 13.
No, both 3 point 6 1 squared and 3 point 6 2 squared are less than 13.
No, both 3.612
and 3.622
are greater than 13.
No, both 3 point 6 1 squared and 3 point 6 2 squared are greater than 13.
is between 3.61 and 3.62. Analyze Walter's estimation. Is he correct? If not, what mistake did he make?(1 point)
Responses
Yes, Walter is correct.
Yes, Walter is correct.
No, 3.612
is less than 13.
No, 3 point 6 1 squared is less than 13.
No, both 3.612
and 3.622
are less than 13.
No, both 3 point 6 1 squared and 3 point 6 2 squared are less than 13.
No, both 3.612
and 3.622
are greater than 13.
No, both 3 point 6 1 squared and 3 point 6 2 squared are greater than 13.
Answers
GPT-4o mini
To determine whether Walter is correct in estimating that \( \sqrt{13} \) is between 3.61 and 3.62, we can square both values to see if they fall below or above 13.
1. Calculate \( 3.61^2 \):
\[
3.61^2 = 12.9921
\]
2. Calculate \( 3.62^2 \):
\[
3.62^2 = 13.0644
\]
Now we can analyze:
- \( 3.61^2 = 12.9921 \) which is **less than** 13.
- \( 3.62^2 = 13.0644 \) which is **greater than** 13.
This means that \( \sqrt{13} \) is indeed between 3.61 and 3.62, so Walter's estimation is correct.
The correct response would be:
**Yes, Walter is correct.**
1. Calculate \( 3.61^2 \):
\[
3.61^2 = 12.9921
\]
2. Calculate \( 3.62^2 \):
\[
3.62^2 = 13.0644
\]
Now we can analyze:
- \( 3.61^2 = 12.9921 \) which is **less than** 13.
- \( 3.62^2 = 13.0644 \) which is **greater than** 13.
This means that \( \sqrt{13} \) is indeed between 3.61 and 3.62, so Walter's estimation is correct.
The correct response would be:
**Yes, Walter is correct.**