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