Hal used the following procedure to find an estimate for 82.5−−−−√ .Step 1: Since 92=81 and 102=100 and 81<82.5<100 , then 82.5−−−−√ is between 9 and 10.Step 2: Since 82.5 is closer to 81, square the tenths closer to 99.02=81.00 9.12=82.81 9.22=84.64 Step 3: Since 81.00<82.5<82.81 , square the hundredths closer to 9.19.082=82.44 9.092=82.62 Step 4: Since 82.5 is closer to 82.62 than it is to 82.44, 9.09 is the best approximation for 82.5−−−−√ .In which step did Hal make an error? NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.(1 point)ResponsesIn step 2, he made a calculation error when squaring.In step 2, he made a calculation error when squaring.In step 4, he made an error in determining which value is closer to 82.5.In step 4, he made an error in determining which value is closer to 82.5.Hal did not make an error.Hal did not make an error.In step 1, 82.5−−−−√ is between 8 and 10 because 82.5−−−−√∼80 and 8×10=80.In step 1, square root of 82 point 5 is between 8 and 10 because square root of 82 point 5 approximates 80 and 8 times 10 is equal to 80.Skip to navigation

Question

Hal used the following procedure to find an estimate for 82.5−−−−√ .Step 1: Since 92=81 and 102=100 and 81<82.5<100 , then 82.5−−−−√ is between 9 and 10.Step 2: Since 82.5 is closer to 81, square the tenths closer to 99.02=81.00 9.12=82.81 9.22=84.64 Step 3: Since 81.00<82.5<82.81 , square the hundredths closer to 9.19.082=82.44 9.092=82.62 Step 4: Since 82.5 is closer to 82.62 than it is to 82.44, 9.09 is the best approximation for 82.5−−−−√ .In which step did Hal make an error? NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.(1 point)ResponsesIn step 2, he made a calculation error when squaring.In step 2, he made a calculation error when squaring.In step 4, he made an error in determining which value is closer to 82.5.In step 4, he made an error in determining which value is closer to 82.5.Hal did not make an error.Hal did not make an error.In step 1, 82.5−−−−√ is between 8 and 10 because 82.5−−−−√∼80 and 8×10=80.In step 1, square root of 82 point 5 is between 8 and 10 because square root of 82 point 5 approximates 80 and 8 times 10 is equal to 80.Skip to navigation

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1 answer
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Answer 1

Bot GPT 4-o mini answered
24 days ago

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 \( 8 \times 10 = 80 \).**