How to find the nth Root of any positive number

[thetechie]

i am new in Java. i would like to know how to find the nth root of any positive number using recursion. Is there any way i can do this without using math.pow()?

[r035198x]

What have you tried?

[thetechie]

public class recursion01 {
	public static void main(String[] args){
		
		double base = 3;
		int exp = 2;
		
		System.out.println(root (base,exp));
		
	}

	private static double root(double base, int exp) {
		if (exp == 0){
			return 1;
		}
		
		else{
			double sum = root(base, exp-1);
			sum = sum * base;
			return sum;
		}
	}
	
}

[r035198x]

If you don't want to use Math.pow then you can use the general nth root algorithm x(k+1) =(1/n)*((n-1)*x(k)+A/pow(x(k),n-1)).

pow with the exponent always integer can be written recursively as

 static double pow(double x, int n) {
        if(n == 0) {
            return 1;
        }
        return x * pow(x, n-1);
    }

Then your function becomes

  private static double nthRoot(int n, double A) {
        double x0 = 1;
        boolean accurate = false;
        while (!accurate) {
            double x1 = (1 / (double)n) * ((n - 1) * x0 + A / pow(x0, n - 1));
            accurate = accurate(x0, x1);
            x0 = x1;
        }
        return x0;
    }
 
    
    private static boolean accurate(double x0, double x1) {
        return Math.abs(x1-x0) < 0.000001;
    }