# Find the Largest N digit perfect square number in Base B

Given two integers N and B, the task is to find the largest N digit numbers of Base B which is a perfect square.

Examples:

Input: N = 2, B = 10
Output: 81
Explanation:
81 is the largest 2-digit perfect square in base 10.

Input: N = 1, B = 8
Output: 4
Explanation:
4 is the largest 1 digit Octal number which is also a perfect square.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The largest number N in base B is given by . So if we find the square root of this number in integer form and then we have to again do its square then it will be the largest perfect square of N digits which is given by the formula: .

Below is the implementation of the above approach:

## C++

 // C++ implementation to find Largest  // N digit perfect square number in Base B     #include  using namespace std;     // Function to find the  // largest N digit number  void nDigitPerfectSquares(int n, int b)  {      // Largest n-digit perfect square      int largest          = pow(ceil(sqrt(pow(b, n))) - 1, 2);         // Print the result      cout << largest;  }     // Driver Code  int main()  {      int N = 1, B = 8;         nDigitPerfectSquares(N, B);         return 0;  }

## Java

 // Java implementation to find largest N  // digit perfect square number in base B  import java.io.*;   import java.util.*;      class GFG {         // Function to find the  // largest N digit number  static double nDigitPerfectSquares(int n, int b)  {             // Largest n-digit perfect square      double largest = Math.pow(Math.ceil                               (Math.sqrt                               (Math.pow(b, n))) - 1, 2);             // Print the result      return largest;  }     // Driver code   public static void main(String[] args)   {       int N = 1, B = 8;      System.out.println(nDigitPerfectSquares(N, B));  }   }      // This code is contributed by coder001

## Python3

 # Python3 implementation to find the largest   # N digit perfect square number in base B   import math     # Function to find the   # largest N digit number   def nDigitPerfectSquares(n, b):          # Largest n-digit perfect square       largest = pow(math.ceil                   (math.sqrt(pow(b, n))) - 1, 2)          # Print the result       print(largest)      # Driver Code   N = 1 B = 8    nDigitPerfectSquares(N, B)     # This code is contributed by divyamohan123

## C#

 // C# implementation to find largest N  // digit perfect square number in base B  using System;     class GFG {         // Function to find the  // largest N digit number  static double nDigitPerfectSquares(int n, int b)  {             // Largest n-digit perfect square      double largest = Math.Pow(Math.Ceiling                               (Math.Sqrt                               (Math.Pow(b, n))) - 1, 2);             // Print the result      return largest;  }     // Driver code   public static void Main(String[] args)   {       int N = 1, B = 8;             Console.WriteLine(nDigitPerfectSquares(N, B));  }   }      // This code is contributed by PrinciRaj1992

Output:

4


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.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

1

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.