16Square
- Reason
- 4 * 4 = 16
Check Perfect Square in Python
What you’ll learn
- What a perfect square means with easy examples.
- How to check a number using an integer loop.
- How to use square root and list perfect squares in a range.
Overview
A perfect square is any number that can be written as k * k. This page shows two checking styles and a live preview.
Two programs
Loop check and square-root-based range scan.
Live preview
Try values like 15, 16, 1, and 0 instantly.
Interview clarity
Know both integer and root-based methods.
Prerequisites
Basic Python loops, integer multiplication, and import usage.
- For-loop and if-condition basics.
- Knowing that
math.isqrtgives integer square root.
What is a perfect square?
A perfect square is a number equal to k squared for some integer k.
Examples: 1, 4, 9, 16, 25. Non-examples: 2, 3, 5, 6.
Quick examples
15Not square
- Reason
- Between 3^2 and 4^2
1Square
- Reason
- 1 * 1 = 1
Live preview
Checks with integer logic, then reports verdict.
Algorithm
Goal: verify if n equals k squared for some integer k.
Loop method
Try i from 0 while i*i <= n and look for exact match.
Square-root method
Use integer root and compare root*root with n.
📜 Pseudocode
Pseudocode
function is_perfect_square_loop(n):
if n < 0:
return false
i = 0
while i * i <= n:
if i * i == n:
return true
i = i + 1
return false1
Integer loop check
Simple and beginner-friendly perfect square check.
python
def is_perfect_square(number: int) -> bool:
if number < 0:
return False
i = 0
while i * i <= number:
if i * i == number:
return True
i += 1
return False
test_number = 16
if is_perfect_square(test_number):
print(f"{test_number} is a perfect square.")
else:
print(f"{test_number} is not a perfect square.")2
Range scan using integer square root
Use math.isqrt and print all perfect squares from 1 to 50.
python
import math
def is_perfect_square(num: int) -> bool:
if num < 0:
return False
root = math.isqrt(num)
return root * root == num
print("Perfect Squares in the Range 1 to 50:")
for i in range(1, 51):
if is_perfect_square(i):
print(i, end=" ")Notes
Prefer integer roots. math.isqrt avoids floating-point rounding issues.
Loop complexity. Loop approach takes O(sqrt(n)) checks.
Negative values. Return false immediately for negatives.
❓ FAQ
A whole number is a perfect square if it equals k * k for some whole number k.
Yes. 1 = 1 * 1.
The loop is easy to understand and avoids floating-point concerns.
It means we only test candidate roots whose square has not passed n.
Yes. It gives exact integer square root and is great for robust checks.
No. Perfect square is about k * k; perfect number is about divisor sums.
🔄 Input / output examples
Try these values in the first example.
| Value | Typical result |
|---|---|
| 16 | Perfect square |
| 15 | Not perfect square |
| 1 | Perfect square |
| 0 | Perfect square |
Edge cases
n = 0
Zero is square
0 = 0 * 0.
Negative n
Not a real integer square
Return false for negatives in this tutorial.
Large values
Avoid float precision pitfalls
Prefer math.isqrt over float sqrt for reliability.
⏱️ Time and space complexity
| Approach | Time (single n) | Extra space |
|---|---|---|
| Loop until i*i > n | O(sqrt(n)) | O(1) |
| isqrt-based check | O(1) practical | O(1) |
| Range 1..U scan | O(U) checks | O(1) |
Summary
- Definition: n is square if n = k * k.
- Methods: integer loop or
math.isqrt. - Remember: 0 and 1 are perfect squares.
Did you know?
A perfect square can be arranged into a square grid with equal rows and columns. The gaps between consecutive squares (1, 4, 9, 16...) are odd numbers (3, 5, 7, 9...).
About the author
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