Perfect Cube Calculator
Determine if a number is a perfect cube and find its cube root
Check Perfect Cube
Enter any integer or decimal number to check if it's a perfect cube
Example Calculations
Perfect Cubes
8: ∛8 = 2, so 2³ = 8 ✓
27: ∛27 = 3, so 3³ = 27 ✓
-8: ∛(-8) = -2, so (-2)³ = -8 ✓
125: ∛125 = 5, so 5³ = 125 ✓
Not Perfect Cubes
100: ∛100 ≈ 4.64 (not integer) ✗
16: ∛16 ≈ 2.52 (not integer) ✗
50: ∛50 ≈ 3.68 (not integer) ✗
200: ∛200 ≈ 5.85 (not integer) ✗
First 10 Perfect Cubes
Perfect Cube Properties
A perfect cube is n³ where n is an integer
Negative numbers can have perfect cubes
0 and 1 are perfect cubes
Cube root of negative = negative result
Understanding Perfect Cubes
What is a Perfect Cube?
A perfect cube is a number that results from multiplying an integer by itself three times. In mathematical terms, if N = a × a × a (or a³) where 'a' is an integer, then N is a perfect cube.
Perfect Cube Formula
N = a³ = a × a × a
Where 'a' is any integer (positive, negative, or zero) and 'N' is the resulting perfect cube.
How to Identify Perfect Cubes
- 1.Calculate the cube root of the number
- 2.Check if the cube root is a whole number
- 3.Verify by cubing the result
Special Cases
Negative Numbers: (-2)³ = -8 (perfect cube)
Zero: 0³ = 0 (perfect cube)
One: 1³ = 1 (perfect cube)
Applications of Perfect Cubes
Volume Calculations
Perfect cubes represent volumes of cubes with integer side lengths
Number Theory
Important in studying cubic equations and algebraic patterns
Problem Solving
Used in mathematical competitions and advanced arithmetic