Calculating the Cube root.

general
1

We all know that we can easily calculate the cube root using pow() func. But the question is how to do it without using this func. or any other such function?

2

If you really don’t want to use any <math.h> function, the easiest is binary search.

double CubeRoot(double x) {
    double left = 0, right = max(1.0, x);  // note that the root for x in [0, 1[ is larger than x.
    double precision = 0.001;
    while (left + precision < right) {
        double r = (left + right) / 2;
        if (r*r*r > x) {
            right = r;
        } else {
            left = r;
        }
    }
    return left;
}

There are more advanced methods like the Newton-Raphson.

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3

You can do it using binary search. let x be the number you have to find the cube root of.
then here is the outline of what you will code :

double hi = max(x, 1), lo = 0, mid;

for (int i = 0; i < 200; ++i) {

mid = (lo + hi)/2.0;

if (mid * mid * mid < x) lo = mid;

else hi = mid;

}

200 is randomly chosen you can choose any big enough number as the value of mid keeps getting closer to x^(1/3) after each iteration.

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4

much better answer than mine :stuck_out_tongue:

5

Note that the nth root for numbers between 0 and 1 is actually larger than the number, e.g. cubic root of 0.5 is 0.8122…
So hi should be max(1, x).

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6

Yeah, I saw that in your answer :slight_smile:

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