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, 3.612
is less than 13.
No, 3 point 6 1 squared is less than 13.

Yes, Walter is correct.
Yes, Walter is correct.

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.

Answer 1

To determine if Walter's estimations are correct, we need to check the squares of the values he proposed (3.61 and 3.62) and see if they are indeed less than or greater than 13.

1. Calculate \(3.61^2\): \[ 3.61 \times 3.61 = 12.9921 \quad (\text{which is less than 13}) \]

2. Calculate \(3.62^2\): \[ 3.62 \times 3.62 = 13.0644 \quad (\text{which is greater than 13}) \]

Given this analysis:

• \(3.61^2 < 13\) (approximately 12.99)
• \(3.62^2 > 13\) (approximately 13.06)

So, Walter's assertion that \( \sqrt{13} \) is between 3.61 and 3.62 is correct.

The response options related to Walter's estimations can be analyzed as follows:

• "No, 3.612 is less than 13." (Correctly states that \(3.61^2 < 13\))
• "No, 3.61 squared is less than 13." (Correctly states that \(3.61^2 < 13\))
• "Yes, Walter is correct." (Correct conclusion)
• "No, both 3.612 and 3.622 are less than 13." (Incorrect)
• "No, both 3.612 and 3.622 are greater than 13." (Incorrect)

Since Walter’s estimation is accurate, the correct choice is: Yes, Walter is correct.