Question
Walter is using the iterative process to determine that \sqrt(13) is between 3.61 and 3.62. Analyze Walter's estimation. Is correct? if not, what mistake did he make?
A. No, 3.61^(2) is less than 13.
B. No, both 3.61^(2) and 3.62(2) are less than 13.
C. No, both 3.61^(2) and 3.62(2) are greater than 13.
D. Yes, Walter is correct.
A. No, 3.61^(2) is less than 13.
B. No, both 3.61^(2) and 3.62(2) are less than 13.
C. No, both 3.61^(2) and 3.62(2) are greater than 13.
D. Yes, Walter is correct.
Answers
GPT-4o mini
To analyze Walter's estimation of \(\sqrt{13}\) being between 3.61 and 3.62, we should evaluate the squares of both 3.61 and 3.62:
- Calculate \(3.61^2\):
\[
3.61^2 = 12.9921
\]
- Calculate \(3.62^2\):
\[
3.62^2 = 13.0644
\]
Now we can see that:
- \(3.61^2 = 12.9921\) is less than 13.
- \(3.62^2 = 13.0644\) is greater than 13.
Thus, based on these calculations, we can conclude that \(\sqrt{13}\) is indeed between 3.61 and 3.62.
Given this analysis, Walter's estimation is **correct**.
The correct answer is:
**D. Yes, Walter is correct.**
- Calculate \(3.61^2\):
\[
3.61^2 = 12.9921
\]
- Calculate \(3.62^2\):
\[
3.62^2 = 13.0644
\]
Now we can see that:
- \(3.61^2 = 12.9921\) is less than 13.
- \(3.62^2 = 13.0644\) is greater than 13.
Thus, based on these calculations, we can conclude that \(\sqrt{13}\) is indeed between 3.61 and 3.62.
Given this analysis, Walter's estimation is **correct**.
The correct answer is:
**D. Yes, Walter is correct.**