What approximation is "best" depends on the required level of accuracy.
11.5326
There is no "best" approximation. The square root is irrational and so it is a non-terminating, non-recurring decimal so adding one more digit will always make it a better approximation.
√40108 = 200.269817996
11.532562594670795889354183238818 round to whatever decimal you want.
20.1
20.10940048555797
I'd say 2.1 or 2.
203 = 8000 Let f(x) = 8132 - x3 then f'(x) = the derivative of f(x) = -3x2 Using Newton-Raphson method, a better estimate is 20 - f(x)/f'(x) = 20 - 132/(-3*202) = 20 + 132/1200 = 20 + 11/100 = 20.11
What approximation is "best" depends on the required level of accuracy.
11.5326
There is no "best" approximation. The square root is irrational and so it is a non-terminating, non-recurring decimal so adding one more digit will always make it a better approximation.
3.16227766 which is about 3.2
√40108 = 200.269817996
which is the best approximation of
11.532562594670795889354183238818 round to whatever decimal you want.
450.00