◻️ Perfect Square Checker

Check whether a positive integer is a perfect square and calculate its nearest integer square root.

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Also available in our Android app, with charts and full breakdown tables.

📘 About the Perfect Square

The calculator finds the integer square root by taking the floor of the mathematical square root.

It then squares that integer to determine whether the original value is a perfect square.

🧮 Formula

Integer square root
r = floor(√n)
Perfect square test
r² = n

Where

  • n = input
  • r = floor(sqrt(n))
  • n is a perfect square when r² = n
Negative numbers are not perfect squares in the real-number system used here.

✏️ Worked example

Is 144 a perfect square?

You enter
Number144
You get
Perfect Square1
Integer Square Root12
Nearest Lower Perfect Square144

Yes. 12 x 12 = 144.

Try this example →

🧭 How to use this calculator

What you enter

  • Number

What you get

  • Perfect Square
  • Integer Square Root
  • Nearest Lower Perfect Square

💡 Examples

  • 25 is a perfect square because 5² = 25.
  • 50 is not a perfect square.
  • 0 is a perfect square.

❓ Frequently asked questions

What is a perfect square?

It is an integer that equals another integer multiplied by itself.

Is zero a perfect square?

Yes, 0 = 0².

What about negative numbers?

They are not real perfect squares.