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 less than 13.
No, both 3 point 6 1 squared and 3 point 6 2 squared are less than 13.

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

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.

No, 3.612
is less than 13.

Answer 1

To check Walter's estimation of \(\sqrt{13}\) being between 3.61 and 3.62, we can square both values:

1. Calculate \(3.61^2\): \[ 3.61 \times 3.61 = 12.9921 \]

2. Calculate \(3.62^2\): \[ 3.62 \times 3.62 = 13.0644 \]

Now we can compare these results to 13:

• \(3.61^2 = 12.9921 < 13\)
• \(3.62^2 = 13.0644 > 13\)

Since \(12.9921 < 13 < 13.0644\), we can conclude that \(3.61 < \sqrt{13} < 3.62\).

Given this analysis, Walter's estimation is indeed correct. Thus the correct response is:

Yes, Walter is correct.

Answer 2

are u sure?

Answer 3

Yes, I am confident in the analysis provided.

To summarize:

• We squared both 3.61 and 3.62.
• \(3.61^2 \approx 12.9921\), which is less than 13.
• \(3.62^2 \approx 13.0644\), which is greater than 13.

Since \(12.9921 < 13 < 13.0644\), it confirms that: \[ 3.61 < \sqrt{13} < 3.62 \] Thus, Walter's estimation that \(\sqrt{13}\) is between 3.61 and 3.62 is correct.

If you have any further questions or need clarification, feel free to ask!