bounds of the interval within which must lie allows the value of to be estimated with a greater precision, either by increasing the lower bounds of the interval or decreasing the upper bounds of the interval.
:
: This procedure can be repeated as many times as needed to attain the desired level of precision. Theoretically, by repeating the steps indefinitely, one can arrive at the true value of this square root.

Herons method

The Babylonian method uses an

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