Loading Calculator...
Please wait a moment
Please wait a moment
Calculate cube roots for any number, including negative values. Check for perfect cubes and get step-by-step solutions with verification.
Negative numbers are allowed!
Enter a number to calculate its cube root
Type any number (positive or negative) in the input field. Unlike square roots, cube roots can be calculated for negative numbers!
Click the "Calculate" button or press Enter. The calculator will determine if your number is a perfect cube and show the result.
View the step-by-step solution and verification to understand how the cube root was calculated.
∛x = y where y³ = x
The cube root of x is the number that, when cubed, gives x.
∛(-x) = -∛x
Example: ∛(-8) = -2 because (-2)³ = -8
∛(ab) = ∛a × ∛b
Example: ∛(8×27) = ∛8 × ∛27 = 2 × 3 = 6
∛(a/b) = ∛a / ∛b
Example: ∛(27/8) = ∛27 / ∛8 = 3/2
| Number | Cube | Cube Root | Negative Cube |
|---|---|---|---|
| 1 | 1 | ∛1 = 1 | ∛-1 = -1 |
| 2 | 8 | ∛8 = 2 | ∛-8 = -2 |
| 3 | 27 | ∛27 = 3 | ∛-27 = -3 |
| 4 | 64 | ∛64 = 4 | ∛-64 = -4 |
| 5 | 125 | ∛125 = 5 | ∛-125 = -5 |
| 6 | 216 | ∛216 = 6 | ∛-216 = -6 |
| 7 | 343 | ∛343 = 7 | ∛-343 = -7 |
| 8 | 512 | ∛512 = 8 | ∛-512 = -8 |
| 9 | 729 | ∛729 = 9 | ∛-729 = -9 |
| 10 | 1000 | ∛1000 = 10 | ∛-1000 = -10 |
A cube root of a number x is a value that, when multiplied by itself three times, gives x. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. It's denoted by the symbol ∛.
Yes! Unlike square roots, cube roots of negative numbers are real numbers. For example, ∛(-8) = -2 because (-2) × (-2) × (-2) = -8. This is because multiplying three negative numbers gives a negative result.
A perfect cube is a number that is the cube of an integer. Examples include 1, 8, 27, 64, 125, etc. These numbers have exact integer cube roots. Negative perfect cubes also exist: -1, -8, -27, -64, etc.
Square root asks 'what number times itself equals x?' while cube root asks 'what number times itself three times equals x?' Also, square roots of negative numbers aren't real, but cube roots of negative numbers are real and negative.
To simplify ∛x, factor x into perfect cubes and non-perfect cubes. Take the cube root of perfect cubes outside the radical. For example, ∛(54) = ∛(27×2) = ∛27 × ∛2 = 3∛2.
Cube roots are used in geometry (finding the side of a cube given its volume), physics (calculating dimensions from volume), engineering (scaling problems), and finance (calculating compound interest rates over multiple periods).
Cube roots extend the concept of square roots to three dimensions. While square roots relate to areas of squares, cube roots relate to volumes of cubes. If you know the volume of a cube, the cube root tells you the length of each edge.
One fascinating property of cube roots is that they work with negative numbers. This is because multiplying three negative numbers together gives a negative result. This makes cube roots more versatile than square roots in real number calculations.