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?

Answer 1

To determine whether Walter's estimation of \( \sqrt{13} \) being between 3.61 and 3.62 is correct, we can calculate the squares of 3.61 and 3.62 and see where \( 13 \) falls in relation to these values.

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

2. Calculate \( 3.62^2 \):
\[
3.62^2 = 13.0564
\]

Now we compare these results with 13:
- \( 3.61^2 = 12.9921 \) which is less than 13.
- \( 3.62^2 = 13.0564 \) which is greater than 13.

Since \( 12.9921 < 13 < 13.0564 \), we can conclude that \( \sqrt{13} \) is indeed between 3.61 and 3.62.

Therefore, Walter's estimation that \( \sqrt{13} \) is between 3.61 and 3.62 is correct. He did not make a mistake in this iterative process.