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Useful Computational Methods

Square-roots: How Calculators Find Them

Many electronic calculators have a square-root key. All you do is enter a number and press this key. Here is the theory that calculators use to find the square-roots.

Logarithms in base e are called natural logarithms. Logex is written lnx.
Now, from t(lnx) = ln(xt) and x = elnx, we have x1/n = e(1/n)lnx. For square-roots then, √x = e(1/2)lnx.

You may discern that the method that the calculator uses to find square-roots is really the logarithm method discussed previously, except that the calcualator uses natural logarithms.




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Last updated - December 14, 2003