Estimate square root of 90 to the nearest hundredths place
2 answers:
The method for doing this will depend on the required accuracy of your estimate.
Using linear approximation between 9^2 = 81 and 10^2 = 100, the estimate is
.. 9 +(90-81)/(100-81) = 9 +9/19 ≈ 9.47
Using one round of "Babylonian Method" on the above estimate,
.. (9.47 +90/9.47)/2 ≈ 9.486 ≈ 9.49 . . . . . . actually accurate to the hundredths place
Using derivatives and linear approximation,
.. √90 ≈ √81 +1/(2√81)*(90-81) = 9.50
or
.. √90 ≈ √100 +1/(2√100)*(90 -100) = 9.50
Using linear approximation between 9^2 = 81 and 10^2 = 100, the estimate is
.. 9 +(90-81)/(100-81) = 9 +9/19 ≈ 9.47
Using one round of "Babylonian Method" on the above estimate,
.. (9.47 +90/9.47)/2 ≈ 9.486 ≈ 9.49 . . . . . . actually accurate to the hundredths place
Using derivatives and linear approximation,
.. √90 ≈ √81 +1/(2√81)*(90-81) = 9.50
or
.. √90 ≈ √100 +1/(2√100)*(90 -100) = 9.50
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