C Perfect Square Program

What Is a Perfect Square?

A non-negative integer is a perfect square when it equals some integer k multiplied by itself: n = k × k.

n is a perfect square  ⇔  ∃ integer k ≥ 0 such that k² = n

Examples:
   0 = 0²
   1 = 1²
   9 = 3²
  16 = 4²
  10 → no integer square root

How to Check a Perfect Square in C

Four clear steps — then pick an integer loop or a sqrt-and-verify check.

1. Reject negatives (this tutorial treats only n >= 0).
2. Try candidate roots i = 0, 1, 2, … while i * i <= n.
3. If some i * i == n, return true; if you pass n, return false.
4. Or compute root = (int)sqrt(n) and verify root * root == n.

Pseudocode

function IsPerfectSquare(n):
    if n < 0: return false

    i = 0
    while i * i <= n:
        if i * i == n:
            return true
        i = i + 1

    return false

Cheat Sheet

Keep these facts handy while writing the program.

Live Preview

Enter an integer to see the nearest integer root and the perfect-square check.

n = 16
root = 4
4 × 4 = 16
16 is a perfect square

Worked Walkthrough — n = 16

Try successive integer squares until you match or pass 16.

i = 0 → 0² = 0
i = 1 → 1² = 1
i = 2 → 2² = 4
i = 3 → 3² = 9
i = 4 → 4² = 16  ← equal to n

16 is a perfect square

Sqrt path:
  sqrt(16) = 4.0
  root = 4
  4 * 4 == 16 → same answer

C Programs

Start with the integer loop so you never rely on floating point. Use sqrt-and-verify when you want a short, clear check.

#include <stdio.h>

int is_perfect_square(int n)
{
    int i;

    if (n < 0)
        return 0;

    for (i = 0; (long)i * i <= n; i++)
    {
        if (i * i == n)
            return 1;
    }

    return 0;
}

int main(void)
{
    int number = 16;

    if (is_perfect_square(number))
        printf("%d is a perfect square\n", number);
    else
        printf("%d is not a perfect square\n", number);

    return 0;
}

16 is a perfect square

#include <stdio.h>
#include <math.h>

int is_perfect_square(int n)
{
    int root;

    if (n < 0)
        return 0;

    root = (int)sqrt((double)n);
    return root * root == n;
}

int main(void)
{
    printf("%d\n", is_perfect_square(16)); /* 1 */
    printf("%d\n", is_perfect_square(10)); /* 0 */
    printf("%d\n", is_perfect_square(0));  /* 1 */
    printf("%d\n", is_perfect_square(-4)); /* 0 */
    return 0;
}

1
0
1
0

Time and Space Complexity

Both are fine for interviews. Prefer the loop when you must avoid floating-point discussion.

Key Takeaways