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Cube Root Calculator

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The Cube Root Calculator computes the cube root (∛x) of any number, including both positive and negative values. This online calculator instantly provides accurate real and complex cube roots.

Definition of Cube Root

"The cube root of a number is the value that, when multiplied by itself three times, gives the original number."

Mathematically, for a number x, the cube root is y such that:

$$ y^3 = x \quad \text{or} \quad y = \sqrt[3]{x} $$

∛27 = 3
∛−8 = −2
∛64 = 4
∛216 = 6

Some numbers have complex cube roots as well. Our Cube Root Calculator finds both real and imaginary roots instantly.

Practical Example

Find the real and complex cube roots of 1000.

Solution

Real cube root:

$$ x = \sqrt[3]{1000} = 10 $$

Complex roots (all three roots in the complex plane):

Root 1 (Real): 10
Root 2: −5 + 8.660254i
Root 3: −5 − 8.660254i

Properties of Cube Roots

The cube root of an odd perfect cube is odd (∛27 = 3)
The cube root of an even perfect cube is even (∛64 = 4)
The cube root of a negative number is negative (∛−8 = −2)
Every real number has exactly one real cube root

Cube Root Table

Common perfect cube roots:

Number (x)	Cube Root (∛x)
8	2
27	3
64	4
125	5
216	6
1000	10

If a number is not a perfect cube, the calculator will determine whether the roots are real or complex.

How the Cube Root Calculator Works

Input:

Enter any integer or decimal number
Click Calculate

Output:

Displays the real cube root
Shows complex roots if applicable
Provides step-by-step calculations

FAQs

Can I find the cube root of negative numbers?

Yes. Negative numbers have real cube roots. For example, ∛−27 = −3.

What is the difference between square root and cube root?

A square root gives a number that, when squared, equals the original number. A cube root gives a number that, when cubed, equals the original number.

How do you find ∛1728 using prime factorization?

$$ 1728 = 2^6 \times 3^3 $$

$$ \sqrt[3]{1728} = \sqrt[3]{(2^2 \times 3)^3} = 12 $$

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