.
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 9
9.02=81.00
9.12=82.81
9.22=84.64
Step 3: Since 81.00<82.5<82.81
, square the hundredths closer to 9.1
9.082=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?
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(1 point)
Responses
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.
In step 2, he made a calculation error when squaring.
In step 2, he made a calculation error when squaring.
Hal did not make an error.
Hal did not make an error.
In step 4, he made an error in determining which value is closer to 82.5.
1 answer
Hal made an error in step 4.
In that step, he states that 82.5 is closer to 82.62 than it is to 82.44. However, the difference between 82.5 and 82.44 is 0.06, and the difference between 82.5 and 82.62 is only 0.12. Therefore, 82.5 is actually closer to 82.44 than to 82.62.
So, the correct approximation for \( \sqrt{82.5} \) using his method should have been 9.08, not 9.09.
