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

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

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Answer 1 · 2015-04-10T00:15:33

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.

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

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