Perfect Cube
Check if any number is a perfect cube instantly. Enter any integer to see if its cube root is a whole number, with the cube root and factorization shown for perfect cubes.
About This Calculator
Our Perfect Cube Calculator helps you instantly determine whether any number is a perfect cube. A perfect cube is a number that can be expressed as the cube of an integer -- i.e., the result of multiplying an integer by itself three times. This free online tool checks whether the cube root of your number is an integer and displays the cube root when it is.
This calculator is useful for students learning about cube roots and powers in algebra, for teachers preparing math worksheets, and for anyone who needs to quickly check if a number is a perfect cube for number theory, geometry problems, or recreational mathematics. The tool uses the formula N = a^3, where N is your number and a is the potential cube root. If a is an integer, N is a perfect cube.
Key Concepts
- Perfect Cube: A number that equals an integer raised to the power of 3.
- Cube Root: The value that, when multiplied by itself three times, gives the original number.
- Perfect cubes include negative numbers -- for example, (-2)^3 = -8.
- Perfect cubes are also called cube numbers and are the 3D equivalent of square numbers.
Common Perfect Cubes
The first ten positive perfect cubes are: 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000. Larger examples include 8000 (20^3), 27000 (30^3), and 125000 (50^3).
Frequently Asked Questions
What is a perfect cube?
A perfect cube is a number that can be expressed as the product of an integer multiplied by itself three times. For example, 8 is a perfect cube because it equals 2 x 2 x 2, and 27 is a perfect cube because it equals 3 x 3 x 3.
How do you check if a number is a perfect cube?
To check if a number is a perfect cube, calculate its cube root using the cbrt function. If the cube root is an integer (a whole number with no decimal part), then the original number is a perfect cube. For example, the cube root of 216 is 6, which is an integer, so 216 is a perfect cube.
Can a negative number be a perfect cube?
Yes! Unlike square roots, cube roots of negative numbers are real numbers. For example, the cube root of -8 is -2 because (-2) x (-2) x (-2) = -8. So negative numbers like -8, -27, and -216 are all perfect cubes.
Is 0 a perfect cube?
Yes, 0 is a perfect cube because 0 x 0 x 0 = 0. The cube root of 0 is 0, which is an integer.
What is the difference between a perfect square and a perfect cube?
A perfect square is a number obtained by multiplying an integer by itself (e.g., 16 = 4 x 4), while a perfect cube is a number obtained by multiplying an integer by itself three times (e.g., 64 = 4 x 4 x 4). A number can be both a perfect square and a perfect cube if it is a sixth power, like 64 (8^2 = 64 and 4^3 = 64).
Is 1 a perfect cube?
Yes, 1 is a perfect cube because 1 x 1 x 1 = 1. The cube root of 1 is 1, which is an integer.
What are the first 10 perfect cubes?
The first 10 perfect cubes are: 1 (1^3), 8 (2^3), 27 (3^3), 64 (4^3), 125 (5^3), 216 (6^3), 343 (7^3), 512 (8^3), 729 (9^3), and 1000 (10^3).