How do you estimate #sqrt14.5#?

1 Answer
George C.
Feb 19, 2017

#sqrt(14.5) ~~ 3.8#

Explanation:

#3^2 = 9 < 14.5 < 16 = 4^2#

So #sqrt(14.5)# is somewhere between #3# and #4#.

To be more specific we can linearly interpolate - approximating the section of the parabola #y = x^2# between #(3, 9)# and #(4, 16)# using a straight line...

#(14.5-9)/(16-9) = 5.5/7 = 0.7bar(857142) ~~ 0.8#

So #sqrt(14.5) ~~ 3+0.8 = 3.8#

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