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.
Refer Wiki page for more information.
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
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Find Nth positive number whose digital root is X
- Nth root of a number using log
- Smallest root of the equation x^2 + s(x)*x - n = 0, where s(x) is the sum of digits of root x.
- Digital Root (repeated digital sum) of square of an integer using Digital root of the given integer
- Number of digits in the nth number made of given four digits
- Find Nth number in a sequence which is not a multiple of a given number
- Find cubic root of a number
- Primitive root of a prime number n modulo n
- Fast method to calculate inverse square root of a floating point number in IEEE 754 format
- Square root of a number using log
- Find square root of number upto given precision using binary search
- Print a number containing K digits with digital root D
- Square root of a number without using sqrt() function
- Find root of a number using Newton's method
- Find Cube root of a number using Log function
- C program to find square root of a given number
- Floor value Kth root of a number using Recursive Binary Search
- Square root of a number by Repeated Subtraction method
- Min operations to reduce N by multiplying by any number or taking square root
- Check if a number is perfect square without finding square root