∛ Cube Root Calculator
Calculate the cube root (∛x) of any number
Can be positive or negative
Perfect Cubes
What is a Cube Root?
The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
Formula
Example: ∛27 = 3 because 3 × 3 × 3 = 27
Key Properties
- Works with negative numbers: ∛(-8) = -2 (unlike square roots)
- Always one real answer: Every real number has exactly one real cube root
- Inverse of cubing: Cube root "undoes" cubing a number
- Can be written as: ∛x = x^(1/3)
Perfect Cubes
A perfect cube is a number that is the cube of an integer. Examples: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000...
Perfect cubes have integer cube roots. All other numbers have irrational cube roots (decimals that never end or repeat).
Cube Root vs Square Root
Cube Root (∛x)
Square Root (√x)
Real-World Applications
📦 Volume Calculations
- • Find cube side from volume
- • Storage container dimensions
- • Shipping box sizing
- • Building design
🔬 Science
- • Physics calculations
- • Chemistry concentrations
- • Engineering formulas
- • Statistical analysis
📊 Finance
- • Compound growth rates
- • Investment returns
- • Economic modeling
- • Growth projections
🎮 Computer Graphics
- • 3D modeling
- • Game development
- • Animation calculations
- • Rendering algorithms
How to Calculate Cube Roots
Method 1: Perfect Cube Recognition
Memorize perfect cubes (1, 8, 27, 64, 125...) and recognize them instantly.
Method 2: Calculator
Use a scientific calculator's cube root function (usually labeled ∛ or x^(1/3)).
Method 3: Estimation
For ∛50: It's between ∛27=3 and ∛64=4, closer to 4. Try 3.7² ≈ 50.
How to Use This Calculator
Enter Any Number
Type any number (positive or negative) in the input field. Examples: 27, -8, 64, 125
Click Calculate Cube Root
Press the "Calculate Cube Root" button to find ∛x and check if it's a perfect cube.
View Result
See the cube root value, verification, and whether the number is a perfect cube.
Formula
If ∛x = y, then y × y × y = x
Or: ∛x = x^(1/3)
Example 1: ∛27
What number cubed equals 27?
3 × 3 × 3 = 27
Cube Root = 3
Example 2: ∛(-8)
What number cubed equals -8?
(-2) × (-2) × (-2) = -8
Cube Root = -2
Example 3: ∛50
50 is not a perfect cube
Cube Root ≈ 3.684
Verification: 3.684³ ≈ 50
About Cube Root Calculator
The Cube Root Calculator calculates the cube root (∛x) of any number. Unlike square roots, cube roots work with negative numbers and always return a real result. The calculator also verifies if a number is a perfect cube.
When to Use This Calculator
- Mathematics: Solve cube root problems and equations
- Volume Calculations: Find cube side length from volume
- Perfect Cubes: Identify if numbers are perfect cubes (1, 8, 27, 64, 125...)
- Physics: Calculate dimensions from volumes
- Engineering: Solve 3D geometry problems
- Education: Learn cube roots and verify work
Why Use Our Calculator?
- ✅ Perfect Cube Check: Automatically detects perfect cubes
- ✅ Verification: Shows that cube root × cube root × cube root = original
- ✅ Negative Support: Works with negative numbers (unlike square root)
- ✅ Perfect Cube Tables: See common perfect cubes 1³ through 12³
- ✅ Educational: Learn cube root vs square root differences
- ✅ Completely Free: No registration required
Cube Root vs Square Root
Cube roots differ from square roots in important ways:
- Cube Root: Works with negative numbers, one real answer always
- Square Root: No real answer for negatives, ± two answers
- Example: ∛(-8) = -2, but √(-8) has no real solution
Real-World Applications
Volume to Side Length: If a cube has volume 27 units³, find side length: ∛27 = 3 units.
Storage Containers: Calculate dimensions from storage capacity in 3D.
Perfect Cubes: Recognize perfect cubes helps with quick mental math and estimation.
Tips for Using This Calculator
- Cube root of negative numbers gives negative result: ∛(-27) = -3
- Perfect cubes have integer cube roots (1, 8, 27, 64, 125, 216...)
- Use verification to double-check: cube root³ should equal original number
- Click preset buttons (8, 27, 64, 125) for quick perfect cube examples
- Always one real cube root for any real number
Frequently Asked Questions
Can you take the cube root of a negative number?
Yes! Unlike square roots, cube roots of negative numbers are real. ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.
What's the difference between ∛x and √x?
∛x is cube root (multiply 3 times), √x is square root (multiply 2 times). ∛8 = 2, but √8 ≈ 2.83.
How do I type the cube root symbol?
On computer: Alt+251 (Windows) or Option+V (Mac). Or use notation: cbrt(x) or x^(1/3) or x^0.333...
Is 0 a perfect cube?
Yes! 0 = 0³, so ∛0 = 0. Zero is a perfect cube (and also a perfect square, perfect fourth power, etc.).
What's the cube root of 1?
∛1 = 1 because 1 × 1 × 1 = 1. One is a perfect cube.
How many real cube roots does a number have?
Every real number has exactly one real cube root. Unlike square roots, there are no ± signs needed.