Perfect squares – 1, 4, 9, 16, 25 … – appear in geometry (areas of squares), the Pythagorean theorem and factoring. Quick checks on the last digit and digital root rule out most non-squares instantly.
How to use the Perfect Square Calculator
- Your number
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The integer square root is computed exactly for whole numbers of any length; the calculator also explains the last-digit and digital-root tests.
Tips
- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.
Common mistakes to avoid
- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.
Formula
N is a perfect square ⇔ √N is an integer
Squares end in 0, 1, 4, 5, 6 or 9 and have digital root 1, 4, 7 or 9
Worked example
Inputs — Your number: 144.
Results — Result = 144 is a perfect square: 12² = 144; Square root = 12; Quick checks = Last digit 4 can end a square; digital root 9 is allowed (1, 4, 7 or 9).
Key terms
- Perfect square
- The square of an integer.
Frequently asked questions
Is 0 a perfect square?
Yes, 0 = 0².
Can a perfect square end in 2, 3, 7 or 8?
Never.
How many perfect squares are there below 100?
Ten: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 (or nine positive ones).
How many factors does a perfect square have?
An odd number.
What formula does the Perfect Square Calculator use?
N is a perfect square ⇔ √N is an integer.