Square root of 99 ```Name: brandon s pincus Status: N/A Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: What is the square route of 99? 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. hawley Click here to return to the Mathematics Archives

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