Answer:
9.7
Explanation:
An estimate of the square root of 95 can be had by linearly interpolating between the points (81, 9) and (100, 10) on the square root curve. For root r, the interpolated value satisfies ...
(r -9)/(95 -81) = (10 -9)/(100 -81)
r -9 = 14/19 . . . . . multiply by 14
r = 9 + 14/19 ≈ 9.74
The square root of 95 is estimated to be about 9.7.
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Additional comment
The estimate can be refined rapidly by finding the average of this estimate and the quotient of 95 and this estimate.
(9.74 +95/9.74)/2 ≈ 9.7468
Each iteration of this refinement method will double the number of good decimal places.