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

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

Answer 1

To determine whether Walter is correct in estimating that \( \sqrt{13} \) is between 3.61 and 3.62, we can square both values to see if they fall below or above 13.

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

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

Now we can analyze:

• \( 3.61^2 = 12.9921 \) which is less than 13.
• \( 3.62^2 = 13.0644 \) which is greater than 13.

This means that \( \sqrt{13} \) is indeed between 3.61 and 3.62, so Walter's estimation is correct.

The correct response would be: Yes, Walter is correct.