Perfect Square Calculator
Determine if a number is a perfect square and find its square root
Check Perfect Square
Enter any positive integer or decimal number to check if it's a perfect square
Example Calculations
Perfect Squares
4: √4 = 2, so 2² = 4 ✓
9: √9 = 3, so 3² = 9 ✓
16: √16 = 4, so 4² = 16 ✓
25: √25 = 5, so 5² = 25 ✓
100: √100 = 10, so 10² = 100 ✓
Not Perfect Squares
5: √5 ≈ 2.24 (not integer) ✗
8: √8 ≈ 2.83 (not integer) ✗
12: √12 ≈ 3.46 (not integer) ✗
15: √15 ≈ 3.87 (not integer) ✗
50: √50 ≈ 7.07 (not integer) ✗
First 15 Perfect Squares
Perfect Square Properties
A perfect square is n² where n is an integer
Only non-negative numbers can be perfect squares
0 and 1 are perfect squares (0² = 0, 1² = 1)
Perfect squares end in 0, 1, 4, 5, 6, or 9
Understanding Perfect Squares
What is a Perfect Square?
A perfect square is a number that results from multiplying an integer by itself. In mathematical terms, if N = a × a (or a²) where 'a' is a non-negative integer, then N is a perfect square.
Perfect Square Formula
N = a² = a × a
Where 'a' is any non-negative integer and 'N' is the resulting perfect square.
How to Identify Perfect Squares
- 1.Calculate the square root of the number
- 2.Check if the square root is a whole number
- 3.Verify by squaring the result
Quick Tests
Last Digit: Must end in 0, 1, 4, 5, 6, or 9
Digital Root: Must be 1, 4, 7, or 9
Factorization: All prime factors appear an even number of times
Applications of Perfect Squares
Geometry
Perfect squares represent areas of squares with integer side lengths
Algebra
Important in quadratic equations and polynomial factoring
Number Theory
Used in Pythagorean triples and Diophantine equations