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javascriptsqrt

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

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

Solution

  • You could take the last value xi-1 and compare it with the new value xi 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));