Calculate the cube root of any number with precision. Perfect for geometry, engineering, physics, and mathematics applications.
Supports positive, negative, and decimal numbers
Cube Root Result
Input must be a valid number (integers or decimals). Use a leading minus for negatives.
The cube root of a number x is a value that, when multiplied by itself three times, gives x. It's denoted ∛x. For example, ∛8 = 2 because 2 × 2 × 2 = 8. If ∛x = y, then y³ = x.
Unlike square roots, cube roots work for negative numbers! ∛(-27) = -3 because (-3)³ = -27. This is because multiplying three negative numbers gives a negative result, preserving the sign.
An engineer needs a cubic water tank with 1,000 m³ capacity. What should each side length be?
Solution: Side = ∛1000
Result: Side = 10 meters
Verify: 10³ = 1,000 ✓
Perfect Cube
∛27 = 3
Because 3³ = 27
Perfect Cube
∛64 = 4
Because 4³ = 64
Perfect Cube
∛125 = 5
Because 5³ = 125
∛(n³) = n
Cube root of a cube returns the original
∛(a·b) = ∛a · ∛b
Root of product equals product of roots
∛(a/b) = ∛a / ∛b
Root of quotient equals quotient of roots
∛(-x) = -∛x
Odd roots preserve the sign
∛0 = 0
Cube root of zero is zero
∛1 = 1, ∛(-1) = -1
Standard identity properties
Yes! Unlike square roots, cube roots of negative numbers are always real. ∛(-8) = -2 because (-2)³ = -8. This works because multiplying three negative numbers gives a negative result.
Square roots ask 'what squared equals x?' (using index 2), while cube roots ask 'what cubed equals x?' (using index 3). Only cube roots can handle negative numbers in the real number system.
For perfect cubes, memorize common values. For others, use Newton's method: make a guess, cube it, adjust closer. Prime factorization also works: if x = p³, then ∛x = p.
A perfect cube is a number that's the cube of an integer: 1, 8, 27, 64, 125, 216, ... Their cube roots are whole numbers. For example, 1 = 1³, 8 = 2³, 27 = 3³.
Because 0 × 0 × 0 = 0. Zero cubed is zero, so the cube root of zero is zero. This is true for all roots of zero.
Yes. Most cube roots are irrational numbers with infinite non-repeating decimals. Only perfect cubes have rational roots. ∛2 ≈ 1.259921... is irrational.
Basic Cube Root Formula
∛x = y, where y³ = x
y is the number that when cubed equals x
Volume to Side Length
Side = ∛Volume
Find cube side from volume
Verification Method
(∛x)³ = x
Cube the result to verify
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