Quote (nlin @ Nov 2 2013 12:36am)

Linear approximations use the derivative to attempt to estimate rough values.

In this case you know sqrt(49) = 7

Assume

f(x) = sqrt(x)

f'(x) = 1/2 x^(-1/2)

using taylor's theorem:
f(x) ~ f(a) + f'(a) * (x-a)

sqrt(50) = f(50) ~ f(49) + f'(49)  *  (50-49)
= sqrt(49) + 1/2*49^(-1/2) * 1
=7 + 1/14
~7.0714

sqrt(50) ~ 7.0711 so we're pretty close

Quote (feanur @ Nov 1 2013 06:59pm)

Minor mistake fixed. Notice that this kind of linear approximation is very good if your closed to a point where a precise calculation is possible ( 50 is closed to 49 = 7² ).