Rough Estimation
Many of the methods for calculating square roots of a positive real number S require an initial seed value. If the initial value is too far from the actual square root, the calculation will be slowed down. It is therefore useful to have a rough estimate, which may be very inaccurate but easy to calculate. If S ≥ 1, let D be the number of digits to the left of the decimal point. If S < 1, let D be the negative of the number of zeros to the immediate right of the decimal point. Then the rough estimation is this:
- If D is odd, D = 2n + 1, then use
- If D is even, D = 2n + 2, then use
Two and six are used because they approximate the geometric means of the lowest and highest possible values with the given number of digits: and
When working in the binary numeral system (as computers do internally), an alternative method is to use (here D is the number of binary digits).
Read more about this topic: Methods Of Computing Square Roots
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