How do you use the square roots of 144 and 169 to estimate the square root of 154?

1 Answer
Apr 10, 2015

Since #sqrt144 = 12# and #sqrt169 = 13#, #f(x) = x^2# is quite steep by this point, and #Deltax = 1# is a small change in x, it is a reasonable assumption to estimate this portion of the graph as linear, and say that:

Difference:
#169 - 144 = 25#

Percent of the way through the difference:
#154 - 144 = 10#
#=> 10/25 = 40%#

Thus a nice estimate for the square root of 154 is 0.4 + 12 = 12.4. The true square root is 12.410, with a -0.0780% error.