Perfect Squares

About this tool

This page lists the perfect squares n² for n from 1 up to 1,000 and checks whether any whole number up to 10¹⁵ is a perfect square. Type a number to get a yes or no answer, its square root (exact for a perfect square, 6 decimals otherwise), the nearest perfect squares below and above with the distance to each, and whether it is also a perfect cube. The list starts with 50 squares, can show cubes beside them, and copies either as lines such as 12² = 144 or as plain numbers 1, 4, 9, 16. The checker uses exact integer arithmetic with BigInt: it finds the whole-number square root r and tests whether r × r equals your number, so a 15-digit number is never rounded into a wrong answer. Only whole numbers from 0 to 1,000,000,000,000,000 can be checked, and the list stops at 1,000². Everything runs in your browser.

Why use it

• Exact for big numbers: BigInt integer arithmetic gives a reliable yes or no for any number up to 10¹⁵.

• Shows how close a number is to the perfect squares on either side, not just yes or no.

• One list covers squares, and optionally cubes, from 1 to 1,000.

• Copies in two formats: one fact per line, or comma-separated numbers for code and documents.

• Prints in tidy columns, with 100 squares on one page.

How to use

1. Type a whole number in the checker box; commas and spaces are ignored.
2. Read the verdict: whether it is a perfect square, which squares it lies between and how far from each, and whether it is a perfect cube.
3. Check the cards for the square root, the nearest perfect squares below and above, and the cube result.
4. Set how many squares to list, from 1 to 1,000, and tick Show cubes to add n³ to each entry.
5. Click Copy list or Copy numbers only to paste the list elsewhere, or Print list for a paper copy in columns.

When it helps

• Checking homework that asks whether a number is a perfect square.
• Simplifying square roots by spotting the largest perfect square factor, such as √72 = √36 × √2 = 6√2.
• Estimating a square root from the squares on either side, such as √150 between 12 and 13.
• Memorizing the squares up to 20² or 25² for mental math and tests.

Examples

Tips

• A number ending in 2, 3, 7 or 8 is never a perfect square, so those can be ruled out at a glance.
• Consecutive squares differ by the odd numbers: 13² − 12² = 169 − 144 = 25 = 2 × 12 + 1.
• Numbers that are both perfect squares and perfect cubes are sixth powers: 1, 64, 729, 4,096 and so on.
• A perfect square that ends in 0 always ends in an even number of zeros, such as 100 or 3,600.
• Use Copy numbers only for a clean sequence like 1, 4, 9, 16, 25 to paste into code.

Frequently Asked Questions

Glossary

Perfect square

The square of a whole number, such as 1, 4, 9 or 16.

Perfect cube

A whole number cubed, such as 8 = 2³ or 27 = 3³.

Square root

The number that gives the original number when multiplied by itself; √144 = 12.

Integer square root

The largest whole number whose square is at most the number; for 150 it is 12.

Sixth power

A number that is both a perfect square and a perfect cube, such as 64 = 2⁶.