Cube Root Calculator
Find ∛x as a decimal and in simplified radical form.
How to use the Cube Root Calculator
- Enter the number.
- Press Calculate. The result updates automatically as you type.
About the Cube Root Calculator
A cube root undoes cubing. If a cube-shaped box holds 1,000 cubic inches, each edge is ∛1000 = 10 inches long. Cube roots come up when you scale volumes: doubling the volume of a sphere or tank only increases its diameter by ∛2, about 26%.
Every real number has exactly one real cube root, positive or negative, because a negative number cubed stays negative. Perfect cubes to remember are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1,000. The calculator returns the decimal value, the exact simplified radical for whole numbers and a check that cubes the answer back.
Formula
∛x = y ⇔ y³ = x ∛x = x^(1/3)
To simplify, pull out the largest perfect-cube factor: ∛54 = ∛(27 × 2) = 3∛2. Unlike square roots, cube roots of negative numbers are real: ∛−27 = −3.
Example calculation
Using the default values:
- Number = 54
the calculator returns:
- Cube root: 3.7797631497
- Simplified radical: 3∛2
- Perfect cube?: No
- Check: 3.77976315³ ≈ 54
Frequently asked questions
What is the cube root of 64?
4, because 4 × 4 × 4 = 64.
Can you take the cube root of a negative number?
Yes. ∛−125 = −5, since (−5)³ = −125.
How do I simplify a cube root?
Find the largest perfect cube that divides the number and move its root outside. ∛250 = ∛(125 × 2) = 5∛2.
Last updated: · Category: Math calculators