Cube Root Calculator – ∛x Calculator
Calculate the cube root of any number
Table of Contents
How to Use
- Enter any number (positive or negative)
- Click calculate to see the cube root
- View the result and verification
- Check if it's an exact cube root
What is a Cube Root?
The cube root of a number x is a value that, when multiplied by itself three times (cubed), equals x. It's written as ∛x or x^(1/3). Unlike square roots, cube roots can be calculated for negative numbers.
Formula: If ∛x = y, then y × y × y = x
Examples
- ∛8 = 2 (because 2 × 2 × 2 = 8)
- ∛27 = 3 (because 3 × 3 × 3 = 27)
- ∛64 = 4 (because 4 × 4 × 4 = 64)
- ∛-8 = -2 (because -2 × -2 × -2 = -8)
- ∛125 = 5 (because 5 × 5 × 5 = 125)
Real-World Applications
- Volume calculations: Finding the side length of a cube given its volume
- Engineering: Scaling calculations and dimensional analysis
- Physics: Inverse cube law calculations
- Finance: Compound interest calculations over three periods
- Computer graphics: 3D transformations and scaling
Properties of Cube Roots
- ∛(a × b) = ∛a × ∛b
- ∛(a/b) = ∛a / ∛b
- ∛(a³) = a
- (∛a)³ = a
- Cube roots of negative numbers are negative
- ∛0 = 0
- ∛1 = 1
Frequently Asked Questions
- Can you take the cube root of a negative number?
- Yes! Unlike square roots, cube roots of negative numbers are real numbers. For example, ∛(-8) = -2 because (-2)³ = -8. This is because multiplying three negative numbers gives a negative result.
- What's the difference between square root and cube root?
- A square root (√x) finds a number that, when multiplied by itself twice, equals x. A cube root (∛x) finds a number that, when multiplied by itself three times, equals x. Square roots of negative numbers are imaginary, but cube roots of negative numbers are real.
- How do I calculate cube root without a calculator?
- For perfect cubes, you can memorize common values (8=2³, 27=3³, 64=4³, etc.). For other numbers, use estimation by finding the nearest perfect cubes, or use the Newton-Raphson method for iterative approximation.
- What is a perfect cube?
- A perfect cube is a number that is the cube of an integer. Examples include 1, 8, 27, 64, 125, 216, etc. These numbers have exact integer cube roots.