To determine whether Walter's estimation is correct, we first need to calculate the value of \(\sqrt{13}\).
Calculating \(\sqrt{13}\):
- \(3.6^2 = 12.96\)
- \(3.7^2 = 13.69\)
From this calculation, we can see that \(\sqrt{13}\) is between 3.6 and 3.7. Therefore, initially, we can narrow down our guess.
Now checking the specific range that Walter provided:
- \(3.61^2 = 12.9921\)
- \(3.62^2 = 13.0644\)
From these calculations, we see that:
- \(3.61^2 < 13 < 3.62^2\)
- This means \(\sqrt{13}\) is indeed between 3.61 and 3.62.
Walter is correct in his estimation that \( \sqrt{13} \) lies between 3.61 and 3.62. There doesn't appear to be a mistake in his estimation based on the information given.
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