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

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.

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.

Answer 1

To analyze Walter's estimation, we need to evaluate the squares of 3.61 and 3.62 to see if they are greater than or less than 13.

1. **Calculating \(3.61^2\)**:
\[
3.61^2 = 12.9921
\]
This value is less than 13.

2. **Calculating \(3.62^2\)**:
\[
3.62^2 = 13.0244
\]
This value is greater than 13.

Since \(3.61^2 < 13 < 3.62^2\), it confirms that \(\sqrt{13}\) is indeed between 3.61 and 3.62.

Now, reviewing the answer options:

- "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."
- "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."

The correct response is: **Yes, Walter is correct.**

Walter's estimation is accurate as \(\sqrt{13}\) is indeed between 3.61 and 3.62.