Question 1036453
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state the linear approximation of sqrt(99.95)
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{{{sqrt(99.95)}}} = {{{sqrt(100 - 0.05)}}} = {{{sqrt(100*(1-0.05/100))}}} = {{{10*sqrt(1 - 0.0005)}}} = {{{10*(1 - 0.0005/2)}}} = 10*(1-0.00025) = 10*0.99975 = 9.9975.


The key moment is this approximation

{{{sqrt(1 - x)}}} = {{{1 - x/2}}} (approximately) which is valid for small values of x  (small comparatively with the value of 1).
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