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++
// 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;
} |
Java
// 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 |
Python3
# 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 |
C#
// 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 |
PHP
<?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 ?> |
Javascript
<script> // Javascript program to find if a // number is Surds or not // Returns true if x
// is Surd number function isSurd(n)
{
for (let i = 2;
i * i <= n; i++)
{
// Try all powers of i
let j = i;
while (j < n)
j = j * i;
if (j == n)
return false ;
}
return true ;
}
// Driver Code
let n = 15;
if (isSurd(n))
document.write( "Yes" );
else
document.write( "No" );
// This code is contributed by rag2127 </script> |
Output:
Yes
Time Complexity: O(?n) as the while loop runs for constant time.
Auxiliary Space: O(1)