Replies:
SQRT(99) is an irrational, approximately equal to 9.95. [I bet you already
knew that it was just a little less than 10] Here's how I came up with
9.95 without using a calculator:
Since 10^2 = 100, SQRT(99) must be 10-d where d is much smaller than 1.
A little algebra:
(10-d)*(10-d)=99
100-20*d+d*d =99
1-20*d+d*d = 0
1-20*d = -d*d, but d {{ 1 (much smaller than), so d*d is even less
and for a good approximation, we can assume it's 0:
1-20*d ~= 0
ergo d = 1/20 = 0.05
The actual value of SQRT(99) is 9.94987, so our approximation is pretty
good.

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