Algo to get the n-th root of a number using a false montecarlo method. Fasle because the random number generator is weak but sufficient.

nrt.js

// By Corentin Derbré

function pow(num, exp) {
  let ret = num
  for (let j = 1; j < exp; j++) {
    ret *= num
  }
  return ret
}

function isEven(num) {
  return !( num & 1 )
}

function random(seed1, seed2) {
  let rand
  if (isEven(seed1) && isEven(seed2)) {
    rand = 0.01
  }
  else if (isEven(seed1) && !isEven(seed2)) {
    rand = 0.33
  } 
  else if (!isEven(seed1) && isEven(seed2)) {
    rand = 0.66
  }
  else if (!isEven(seed1) && !isEven(seed2)) {
    rand = 0.99
  }
  return rand
}

function nrt(num, root) {
  if (num < 0 && isEven(root)) {
    return undefined
  }
  let sign = 1
  if (num < 0) {
    num *= -1
    sign *= -1
  }

  const tries = 1000
  let upperBound = num + 1
  let lowerBound = 0
  let guess = random(upperBound, upperBound * 0.23) * upperBound + lowerBound
  for (let i = 0; i < tries; i++) {
    if ( pow(guess, root) < num ) {
      lowerBound = guess
    }
    else {
      upperBound = guess
    }
    guess = random(upperBound, guess) * ( upperBound - lowerBound ) + lowerBound
  }
  return guess * sign
}

console.log(nrt(-1243, 6)) // unfedined
console.log(nrt(81234, 7)) // 5.0279519632
console.log(nrt(-2438, 7)) // -3.0469263549
console.log(nrt(81, 2)) // 9
console.log(nrt(85729437539874902, 4)) // 17111.279829679
console.log(nrt(0, 1)) // 0
console.log(nrt(0, 2)) // 0
console.log(nrt(0, 3)) // 0
console.log(nrt(1, 1)) // 1
console.log(nrt(1, 2)) // 1
console.log(nrt(1, 5)) // 1
console.log(nrt(314, 1)) // 314
console.log(nrt(165.32, 3)) // 5.488349996236