Cube Root Calculator
Calculate cube root ∛x with step-by-step solutions and perfect cube identification
∛ Cube Root Calculator
∛27 = ?
Formula
∛x = y ⟺ y³ = x
Where:
- ∛x =Cube root of x
- y =Result value
- y³ =y cubed (y × y × y)
- Perfect cube =Integer whose cube root is an integer
- ∛(-x) == -∛x (for positive x)
About Cube Roots
The cube root ∛x is the number that, when multiplied by itself three times, gives x. Unlike square roots, cube roots can be calculated for negative numbers.
Perfect Cubes (1-10):
1³ = 1
6³ = 216
2³ = 8
7³ = 343
3³ = 27
8³ = 512
4³ = 64
9³ = 729
5³ = 125
10³ = 1000
Properties:
- • ∛(x³) = x for all real numbers x
- • ∛(-x) = -∛x (cube roots preserve sign)
- • ∛(xy) = ∛x × ∛y
- • ∛(x/y) = ∛x / ∛y (y ≠ 0)
- • ∛0 = 0, ∛1 = 1, ∛(-1) = -1
Applications:
- • Volume calculations (cube side length from volume)
- • Scaling in 3D graphics and modeling
- • Physics: relationship between mass and volume
- • Engineering: structural design calculations
- • Finance: compound interest with cubic growth