Answer:
a) about 99.8
b) about 11.84
Explanation:
You can make use of the fact that ...
(a +b)² = a² +2ab +b²
Then ...
a) 9.9² = (10 -0.1)² = 100 -2 +.01 = 98.01 . . . . . use 98 as the estimate
Adding this value to 1.79 gives ...
98.01 +1.79 = 99.8 . . . . . exact value (see attachment 1)
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b) For square roots, the estimate of the root works in reverse of the estimate of the square.
97.5 = 100 -2.5 ≈ (10 -0.125)² . . . . . where the .125 is 2.5/(2·10)
The √97.5 ≈ 9.88 and the sum is
9.88 +1.96 = 11.84 . . . . . see attachment 2 for a more precise approximation
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The point of this exercise is to help you learn to estimate values that are "near" ones that you know. You know 9.9 is near 10, so you can figure the effect of the slight difference on the result when you use 10 instead of 9.9. Similarly, you know 97.5 is near 100, so you can figure the effect of that small difference.
For crude estimates, you can completely ignore the difference from the "near" value: 9.9^2 +1.79 ≈ 100 +2 ≈ 102; √97.5 +1.96 ≈ 10 +2 ≈ 12.