**Problem Statement:** Given two numbers N and M, find the Nth root of M.

The nth root of a number M is defined as a number X when raised to the power N equals M.

**Example 1:**

Input: N=3 M=27Output:3Explanation:The cube root of 27 is 3.

**Example 2:**

Input:N=2 M=16Output:4Explanation: The square root of 16 is 4

**Example 3:**

Input:N=5 M=243Output:3Explaination:The 5th root of 243 is 3

** Disclaimer**:

*Don’t jump directly to the solution, try it out yourself first.*

**Solution:**

**Nth root** of a number M is defined as a number X when raised to the power N equals to M.

**Approach**: In order to find the Nth root of any given integer we are gonna use Binary Search.

Step 1: Take low and high. Low will be equal to 1 and high will be M. We will take the mid of low and high such that the searching space is reduced using low + high / 2.

Step 2: Make a separate function to multiply mid N times.

Step 3: Run the while loop till (high – low > eps). Take eps as 1e-6, since we have to find answers to 6 decimal places.

Step 4: If the mid is less than M, then we will reduce search space to low and mid. Else, if it is greater than M then search space will be reduced to mid and high.

Step 5: After the loop breaks we will have our answer as low or high.

We have to find the answer to 6 decimals. So, we will have a double 1e-6. We will run the while loop till (high – low > eps). When we will come out of the loop we will have the answer which will be equal to low as well as high.

**Code:**

## C++ Code

```
#include <bits/stdc++.h>
using namespace std;
double multiply(double number, int n) {
double ans = 1.0;
for(int i = 1;i<=n;i++) {
ans = ans * number;
}
return ans;
}
void getNthRoot(int n, int m) {
double low = 1;
double high = m;
double eps = 1e-7;
while((high - low) > eps) {
double mid = (low + high) / 2.0;
if(multiply(mid, n) < m) {
low = mid;
}
else {
high = mid;
}
}
cout <<n<<"th root of "<<m<<" is "<<low<<endl;
}
int main() {
int n=3, m=27;
getNthRoot(n, m);
return 0;
}
```

**Output:** 3th root of 27 is 3

**Time Complexity: N x log(M x 10^d)**

**Space Complexity: O(1)**

## Java Code

```
import java.io.*;
class GFG {
private static double multiply(double number, int n) {
double ans = 1.0;
for(int i = 1;i<=n;i++) {
ans = ans * number;
}
return ans;
}
private static void getNthRoot(int n, int m) {
double low = 1;
double high = m;
double eps = 1e-7;
while((high - low) > eps) {
double mid = (low + high) / 2.0;
if(multiply(mid, n) < m) {
low = mid;
}
else {
high = mid;
}
}
System.out.println(n+"th root of "+m+" is "+low);
}
public static void main (String[] args) {
int n = 3, m = 27;
getNthRoot(n, m);
}
}
```

**Output:** 3th root of 27 is 3

**Time Complexity: N x log(M x 10^d)**

**Space Complexity: O(1)**

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