# 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 = 10Output:81Explanation:

81 is the largest 2-digit perfect square in base 10.Input:N = 1, B = 8Output:4Explanation:

4 is the largest 1 digit Octal number which is also a perfect square.

**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 <bits/stdc++.h>` `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` |

## Javascript

`<script>` `// Javascript implementation to find Largest` `// N digit perfect square number in Base B` `// Function to find the` `// largest N digit number` `function` `nDigitPerfectSquares(n, b)` `{` ` ` `// Largest n-digit perfect square` ` ` `var` `largest` ` ` `= Math.pow(Math.ceil(Math.sqrt(Math.pow(b, n))) - 1, 2);` ` ` `// Print the result` ` ` `document.write(largest);` `}` `// Driver Code` `var` `N = 1, B = 8;` `nDigitPerfectSquares(N, B);` `</script>` |

**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. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.