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# Surd number

• Last Updated : 24 Aug, 2022

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 âˆšn and check if any power is equal n or not.

## C++

 `// CPP program to find if a number is ` `// Surds or not` `#include ` `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

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## Javascript

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Output:

`Yes`

Time Complexity: O(âˆšn) as the while loop runs for constant time.

Auxiliary Space: O(1)

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