Other Methods
Finding is the same as solving the equation . Therefore, any general numerical root-finding algorithm can be used. Newton's method, for example, reduces in this case to the Babylonian method. Other methods are less efficient than the ones presented above.
A completely different method for computing the square root is based on the CORDIC algorithm, which uses only very simple operations (addition, subtraction, bitshift and table lookup, but no multiplication).
Read more about this topic: Methods Of Computing Square Roots
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—Thomas Henry Huxley (1825–95)