It is about 9.487 rounded to 3 decimal places
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4.6 is a better approximation to the square root of 21.
11.5326
The square root of six is irrational. Do you mean a rational approximation?
The approximation of square root of 563 is (261 + (1 / 261)) / 11 From : Indonesia
What approximation is "best" depends on the required level of accuracy.