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

Answer 1

You can use the fact that the square roots of 144 and 169 are 12 and 13, respectively, to estimate the square root of 154. Since 154 is closer to 144 than to 169, you can conclude that the square root of 154 is slightly greater than 12 but less than 13. Therefore, you can estimate the square root of 154 to be around 12.4 or 12.5.

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Answer 2

Eva Abramson

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.