[removed] Calculate the nth root of a number

Question

I\'m trying to get the nth root of a number using JavaScript, but I don\'t see a way to do it using the built in Math object. Am I overlooking something?
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Answer 1

The n-th root of x is a number r such that r to the power of 1/n is x.

In real numbers, there are some subcases:

• There are two solutions (same value with opposite sign) when x is positive and r is even.
• There is one positive solution when x is positive and r is odd.
• There is one negative solution when x is negative and r is odd.
• There is no solution when x is negative and r is even.

Since Math.pow doesn't like a negative base with a non-integer exponent, you can use

function nthRoot(x, n) {
  if(x < 0 && n%2 != 1) return NaN; // Not well defined
  return (x < 0 ? -1 : 1) * Math.pow(Math.abs(x), 1/n);
}

Examples:

nthRoot(+4, 2); // 2 (the positive is chosen, but -2 is a solution too)
nthRoot(+8, 3); // 2 (this is the only solution)
nthRoot(-8, 3); // -2 (this is the only solution)
nthRoot(-4, 2); // NaN (there is no solution)

Answer 2

Can you use something like this?

Math.pow(n, 1/root);

eg.

Math.pow(25, 1/2) == 5

Answer 3

I have written an algorithm but it is slow when you need many numbers after the point:

https://github.com/am-trouzine/Arithmetic-algorithms-in-different-numeral-systems

NRoot(orginal, nthRoot, base, numbersAfterPoint);

The function returns a string.

E.g.

var original = 1000;
var fourthRoot = NRoot(original, 4, 10, 32);
console.log(fourthRoot); 
//5.62341325190349080394951039776481