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Hal made an error in step 1. The square root of 82.5 is actually between 8 and 10, not 9 and 10.
The reasoning behind this is that \(8^2 = 64\) and \(10^2 = 100\). Since \(82.5\) falls between \(64\) and \(100\), the correct lower bound for \( \sqrt{82.5} \) should be \(8\), not \(9\). Therefore, the initial assumption in step 1 was incorrect, which led to further errors in subsequent steps.
Thus, the correct response is:
**In step 1, \( \sqrt{82.5} \) is between 8 and 10 because \( 82.5 \) is closer to 80, and \( 8 \times 10 = 80 \).**