Check Perfect Square Using Sum of Odd Numbers in Python

Program Overview

This Python program checks whether a given number is a perfect square.
Instead of using square roots, it uses a mathematical property: A number is a perfect square if it equals the sum of consecutive odd numbers starting from 1.
Examples:
- √9 = 1 + 3 + 5 - √16 = 1 + 3 + 5 + 7 - √4 = 1 + 3

Python Code:

def is_perfect_square_by_odd_sum(n):
    total = 0
    odd = 1
    while total < n:
        total += odd
        odd += 2
    return total == n

# Run the program
num = int(input("Enter a number: "))
if is_perfect_square_by_odd_sum(num):
    print(f"{num} is a perfect square.")
else:
    print(f"{num} is not a perfect square.")

Sample Output:

Enter a number: 16  
16 is a perfect square.

Enter a number: 20  
20 is not a perfect square.

Step-by-Step Explanation:

- Start with the first odd number: 1
- Keep adding consecutive odd numbers: 1, 3, 5, 7, ...
- Stop when the total reaches or exceeds the input number
- If the total equals the input, it's a perfect square