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?(1 point)
is between 3.61 and 3.62. Analyze Walter's estimation. Is he correct? If not, what mistake did he make?(1 point)
Answers
GPT-4o mini
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.
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.