How find square root n by computing the next Xi term on javascript

Question

Write the function sqrt(A) for computing square root of positive real numbers using next numerical method xi+1 = (1/2) * (xi +(A/xi)). Where the A - input rial number; On zero iteration next statements have been taken: x0 = A; The error should be at least 10^-6

Answer 1

Looks like your requirement is not just finding the square root of a number. If by any chance that is your requirement, use Math.sqrt.

If your requirement is to implement a function to find the square root for educational purpose, what you need is to write a recursive function as below. Modify the code as required to support error at 10^-6

function sqrt(A, i = 0) {
  if (i === 0)
    return A;

  let prev = sqrt(A, i - 1);
  return 0.5 * (prev + (A / prev));
}

console.log(sqrt(2,1000));
console.log(sqrt(3,1000));
console.log(sqrt(9,1000));
console.log(sqrt(25,1000));

Answer 2

You could take the last value x_i-1 and compare it with the new value x_i instead of using a loop counter.

function sqrt(a, x = 1) {    // take 1 for x(0) as start value for recursion
    var y = (x + a / x) / 2; // prepare next value x(i+1)

    if (x === y) {           // exit condition
        return x;
    }
    return sqrt(a, y);       // tail call optimization 
}                            // https://stackoverflow.com/q/310974/1447675

console.log(sqrt(2));
console.log(sqrt(10));
console.log(sqrt(9));
console.log(sqrt(25));