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 ?n and check if any power is equal n or not.
C++
#include <bits/stdc++.h>
using namespace std;
bool isSurd(int n)
{
for (int i=2; i*i<=n; i++)
{
int j = i;
while (j < n)
j = j * i;
if (j == n)
return false;
}
return true;
}
int main()
{
int n = 15;
if (isSurd(n))
cout << "Yes";
else
cout << "No";
return 0;
}
|
Java
class GFG
{
static boolean isSurd(int n)
{
for (int i = 2;
i * i <= n; i++)
{
int j = i;
while (j < n)
j = j * i;
if (j == n)
return false;
}
return true;
}
public static void main(String args[])
{
int n = 15;
if (isSurd(n))
System.out.println("Yes");
else
System.out.println("No");
}
}
|
Python3
def isSurd(n) :
i = 2
for i in range(2, (i * i) + 1) :
j = i
while (j < n) :
j = j * i
if (j == n) :
return False
return True
if __name__ == "__main__" :
n = 15
if (isSurd(n)) :
print("Yes")
else :
print("No")
|
C#
using System;
class GFG
{
static bool isSurd(int n)
{
for (int i = 2;
i * i <= n; i++)
{
int j = i;
while (j < n)
j = j * i;
if (j == n)
return false;
}
return true;
}
public static void Main()
{
int n = 15;
if (isSurd(n))
Console.Write("Yes");
else
Console.Write("No");
}
}
|
PHP
<?php
function isSurd($n)
{
for ($i = 2;
$i * $i <= $n; $i++)
{
$j = $i;
while ($j < $n)
$j = $j * $i;
if ($j == $n)
return false;
}
return true;
}
$n = 15;
if (isSurd($n))
echo ("Yes");
else
echo ("No");
?>
|
Javascript
<script>
function isSurd(n)
{
for (let i = 2;
i * i <= n; i++)
{
let j = i;
while (j < n)
j = j * i;
if (j == n)
return false;
}
return true;
}
let n = 15;
if (isSurd(n))
document.write("Yes");
else
document.write("No");
</script>
|
Time Complexity: O(?n) as the while loop runs for constant time.
Auxiliary Space: O(1)
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