What approximation is "best" depends on the required level of accuracy.
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√40108 = 200.269817996
200.2698....
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.
11.532562594670795889354183238818 round to whatever decimal you want.