Surd number

A number is said to be Surd if its square root, cube root, etc are not integers. For example, 9 is not a Surd as square root of 9 is 3, but 5 is Surd as square root of 5 is not integer. Similarly 8 is not a Surd (Cube root of 8 is integer), but 7 is.

Given a range, find if it is Surds or not
Examples:

Input : 4
Output : No
4 is not a Surd number as its square root is
an integer.

Input : 5
Output : Yes
5 is a Surd number as its square root is not an integer.

Input : 8
Output : No
8 is not a Surd number as cube root of 8
is an integer.

The idea is to try every power of all numbers from 2 to √n and check if any power is equal n or not.



C++

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// CPP program to find if a number is 
// Surds or not
#include <bits/stdc++.h>
using namespace std;
  
// Returns true if x is Surd number
bool isSurd(int n)
{  
    for (int i=2; i*i<=n; i++)
    {
       // Try all powers of i
       int j = i;
       while (j < n)              
          j = j * i;
  
       if (j == n)
          return false;
    }
  
    return true;
}
  
// driver code 
int main()
{  
    int n = 15;
    if (isSurd(n))
       cout << "Yes";
    else
       cout << "No";
    return 0;
}

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Java

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// Java program to find if a
// number is Surds or not
  
class GFG
{
  
// Returns true if x
// is Surd number
static boolean isSurd(int n)
    for (int i = 2
             i * i <= n; i++)
    {
        // Try all powers of i
        int j = i;
        while (j < n)             
            j = j * i;
      
        if (j == n)
            return false;
    }
  
    return true;
}
  
// Driver Code 
public static void main(String args[])
    int n = 15;
    if (isSurd(n))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
  
// This code is contributed
// by Ankita_Saini

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Python3

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# Python3 program to find 
# if a number is Surd or not.
  
# define a isSurd function which
# Returns true if x is Surd number.
def isSurd(n) :
      
    i = 2
    for i in range(2, (i * i) + 1) :
          
        # Try all powers of i
        j = i
        while (j < n) :
            j = j * i
  
        if (j == n) :
            return False
      
    return True
  
# Driver code
if __name__ == "__main__" :
      
    n = 15
      
    if (isSurd(n)) :
        print("Yes")
          
    else :
        print("No")
  
# This code is contributed 
# by Ankit Rai1

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C#

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// C# program to find if a
// number is Surds or not
using System;
  
class GFG
{
  
// Returns true if x
// is Surd number
static bool isSurd(int n)
    for (int i = 2; 
             i * i <= n; i++)
    {
        // Try all powers of i
        int j = i;
        while (j < n)             
            j = j * i;
      
        if (j == n)
            return false;
    }
  
    return true;
}
  
// Driver Code 
public static void Main()
    int n = 15;
    if (isSurd(n))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
  
// This code is contributed
// by ChitraNayal

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PHP

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<?php
// PHP program to find if 
// a number is Surds or not
  
// Returns true if 
// x is Surd number
function isSurd($n)
    for ($i = 2; 
         $i * $i <= $n; $i++)
    {
    // Try all powers of i
    $j = $i;
    while ($j < $n)             
        $j = $j * $i;
  
    if ($j == $n)
        return false;
    }
  
    return true;
}
  
// Driver code 
$n = 15;
if (isSurd($n))
    echo ("Yes");
else
    echo ("No");
  
// This code is contributed 
// by Shivi_Aggarwal 
?>

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Output:

Yes


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