Walter is using the iterative process to determine that 13−−√

Question

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.