How to find the root of any number in any base?

Question

Algorithms

I found such a code, but for the root of the 4th degree of 8 it freezes

function sqrt(a, b) {
    if(b<2) return a
    let num = a;
    let rootDegree = b;
    let eps = 0.00001;            //допустимая погрешность
    let root = num / rootDegree;  //начальное приближение корня
    let rn = num;                 //значение корня последовательным делением
    while(Math.abs(root - rn) >= eps){
        rn = num;
        for(let i = 1; i < rootDegree; i++){
            rn = rn / root;
        }
        root = 0.5 * ( rn + root);
    }
    return root;
}

Answer 1

Algorithm for finding the root of the nth degree