Cube Root Calculator
Calculate cube roots and nth roots with step-by-step solutions
Calculate Root or Power
3 = cube root, 2 = square root, etc.
Negative numbers are allowed for odd roots
Result
Examples
Perfect Cube Example
Problem: Find the cube root of 216
Solution: ∛216 = 6
Verification: 6³ = 6 × 6 × 6 = 216 ✓
Note: 216 is a perfect cube
Real-World Application
Problem: A cube has a volume of 64 cm³. What is the edge length?
Setup: Volume = edge³, so edge = ∛(volume)
Calculation: edge = ∛64 = 4 cm
Answer: Each edge of the cube is 4 cm long
Perfect Cubes (1-10)
Common Non-Perfect Cube Roots
Cube Root Properties
∛(a × b) = ∛a × ∛b
∛(a/b) = ∛a / ∛b
Cube roots of negative numbers are negative
∛x = x^(1/3)
Every real number has exactly one real cube root
Understanding Cube Roots
What is a Cube Root?
The cube root of a number x is a value that, when multiplied by itself three times, gives x. If y is the cube root of x, then y³ = x. This is written as ∛x = y.
Perfect Cubes
Perfect cubes are integers that result from cubing whole numbers. For example, 8 is a perfect cube because 2³ = 8. Perfect cubes have exact integer cube roots.
Geometric Interpretation
In geometry, if a cube has volume V, then its edge length is ∛V. This makes cube roots very useful in three-dimensional problems.
Key Properties
- •Unlike square roots, cube roots of negative numbers are real and negative
- •The cube root function passes through the origin (0,0)
- •Cube root is the inverse operation of cubing
Applications
- •Calculating dimensions from volume
- •Engineering and physics calculations
- •Computer graphics and 3D modeling