9514 1404 393
Answer:
see attached for a plot
14.44, 15.21, 3.8727² ≈ 14.99780529
Step-by-step explanation:
(3.8)² = 14.44
(3.9)² = 15.21
The root of 15 will be approximately at the spot where the line between these values crosses 15.
We can see the slope of the square function is approximately ...
m = (15.21 -14.44)/(3.9 -3.8) = 0.77/0.1 = 7.7
Then the value we need to add to 3.8 will be ...
(15.00 -14.44)/7.7 = 0.56/7.7 ≈ 0.0727
An approximation of the root is 3.8727.
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Additional comment
Here, the location we plotted for √15 is "exact." We're not sure what original approximation you're trying to better. We chose to use linear interpolation between the points (3.8, 14.44), (3.9, 15.21) to estimate the value of 'x' that would give x^2 = 15. (There are other, better, ways to refine the estimate of the root.)
