Given two numbers N and A, find N-th root of A. In mathematics, Nth root of a number A is a real number that gives A, when we raise it to integer power N. These roots are used in Number Theory and other advanced branches of mathematics.
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Input : A = 81 N = 4 Output : 3 3^4 = 81
As this problem involves a real valued function A^(1/N) we can solve this using Newton’s method, which starts with an initial guess and iteratively shift towards the result.
We can derive a relation between two consecutive values of iteration using Newton’s method as follows,
according to newton’s method x(K+1) = x(K) – f(x) / f’(x) here f(x) = x^(N) – A so f’(x) = N*x^(N - 1) and x(K) denoted the value of x at Kth iteration putting the values and simplifying we get, x(K + 1) = (1 / N) * ((N - 1) * x(K) + A / x(K) ^ (N - 1))
Using above relation, we can solve the given problem. In below code we iterate over values of x, until difference between two consecutive values of x become lower than desired accuracy.
Below is the implementation of above approach:
Nth root is 3
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