Here is an implementation of a square root function in JavaScript using Newton's method.

sqrt.js

var sqrt = function(x) {
  var isGoodEnough = function(guess) {
    return Math.abs(guess * guess - x) / x < 0.001;
  };
  
  var improve = function(guess) {
    return (guess + x / guess) / 2;
  };
  
  var sqrIter = function(guess) {
    return (isGoodEnough(guess)) ? guess : sqrIter(improve(guess))
  };
  
  return sqrIter(1.0);
};

console.log(
  Math.sqrt(1000),
  sqrt(1000)
);