Cube Root Calculator - Find ∛x
Result:
Welcome to our Cube Root Calculator. This tool calculates the cube root of any real number, including negative numbers which have real cube roots.
What is a Cube Root?
A cube root of a number x is a value that, when cubed (multiplied by itself three times), gives x. It's denoted as ∛x.
Understanding Cube Roots
The cube root operation is the inverse of cubing a number:
- ∛8 = 2 because 2³ = 8
- ∛27 = 3 because 3³ = 27
- ∛(-8) = -2 because (-2)³ = -8
Key Properties
Real for all inputs: Unlike square roots
Preserves sign: ∛(-x) = -∛x
Perfect cubes: 1, 8, 27, 64, 125...
Fractional form: ∛x = x^(1/3)
Applications
Volume calculations: Side from volume
Engineering: Scaling relationships
Physics: Dimensional analysis
Mathematics: Radical equations
Perfect Cubes
Some numbers have exact cube roots (perfect cubes):
- ∛1 = 1
- ∛8 = 2
- ∛27 = 3
- ∛64 = 4
- ∛125 = 5
- ∛(-1) = -1
- ∛(-8) = -2
- ∛(-27) = -3
- ∛(-64) = -4
- ∛(-125) = -5
Examples
Perfect Cube
∛64 = 4
4 × 4 × 4 = 64Negative Number
∛(-27) = -3
(-3)³ = -27Non-Perfect
∛10 ≈ 2.154435
Decimal approximationFind Calculator
Popular Calculators
Other Calculators
