Babylonian Square Root Math
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So let s try 1 41 squared lower than 2 but 1 42 oh larger then square root 2 must start off with 1 41.
Babylonian square root math. This method can be derived from but predates newton raphson method. A get the next approximation for root using average of x and y b set y n x. The babylonian square root algorithm the iterative method is called the babylonian method for finding square roots or sometimes hero s method. Babylonian method of computing square roots 1 description to compute the square rootof a number which lies between 0 and 2 one may use a method of successive approximations which involves only the operations of squaring and averaging.
1 start with an arbitrary positive start value x the closer to the root the better. Babylonian method for square root last updated. The basis of method is the binomial identity. For other numbers it s not as easy but the ancient babylonians seemed to know how to calculate them pretty accurately see the figure and caption.
Here s how it works. The babylonian method is one of the fastest converging methods for computing square roots but it can be somewhat inconvenient. 1 4 square is 1 96 just slightly below 2. Or go through this in your head.
The square root of a number s is denoted s s with the property that s s s s s s. Do following until desired approximation is achieved. Mini lesson on solving square roots using the babylonian method.
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