Analyzing an Estimation Walter used the iterative process to determine that \( \sqrt{13} \) is between 3.61 and 3.62 . Analyze Walter's estimation. Is he correct? If not, what was his mistake? Yes, Walter is correct. No, \( 3.61^{2} \) is less than 13 . No, both \( 3.61^{2} \) and \( 3.62^{2} \) are greater than 13 . No, both \( 3.61^{2} \) and \( 3.62^{2} \) are less than 13 .

Walter's estimation places \( \sqrt{13} \) between 3.61 and 3.62, but he made a mistake in his analysis. To check this, we can square both endpoints. Squaring 3.61 gives us approximately 13.0321, and squaring 3.62 gives us roughly 13.0644. Both of these values are greater than 13. Thus, Walter's estimation is not correct because it should lie between a number whose square is less than 13 and a number whose square is greater than 13. To accurately find \( \sqrt{13} \), Walter could start by squaring whole numbers around 3.6, like checking 3.6 (which is 12.96) and 3.7 (which is 13.69). This would show that \( \sqrt{13} \) is indeed between 3.6 and 3.7, helping him refine his estimation process. Keeping the endpoint squares in check will avoid this common pitfall!