https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method

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Example

To calculate √S, where S = 125348, to six significant figures, use the rough estimation method above to get
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Therefore, √125348 ≈ 354.045.

Uniswap 中用法

  1. // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
  2.     function sqrt(uint y) internal pure returns (uint z) {
  3.         if (y > 3) {
  4.             z = y;
  5.             uint x = y / 2 + 1;
  6.             while (x < z) {
  7.                 z = x;
  8.                 x = (y / x + x) / 2;
  9.             }
  10.         } else if (y != 0) {
  11.             z = 1;
  12.         }
  13.     }