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The cube root of a number is a value that, when multiplied by itself three times, gives the original number. This calculator finds the cube root of any real number you input.

What is a Cube Root?

The cube root of a number x is a number y such that y × y × y = x. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. Cube roots are the inverse operation of cubing a number.

Unlike square roots, cube roots exist for all real numbers. For positive numbers, there's one real cube root. For negative numbers, there's one real cube root as well (e.g., the cube root of -8 is -2).

How to Calculate Cube Roots

There are several methods to find cube roots:

Prime Factorization: Break down the number into prime factors and group them in triplets.
Estimation: Use trial and error to find a number that, when cubed, is close to the target number.
Calculator: Use a calculator or programming function to compute the cube root directly.

For most practical purposes, using a calculator is the most efficient method.

Formula

The cube root of a number x can be expressed as:

∛x = y, where y × y × y = x

The cube root function is continuous and differentiable everywhere on the real number line. It's a strictly increasing function, meaning that as x increases, ∛x also increases.

Examples

Example 1: Positive Number

Find the cube root of 64.

Solution: 4 × 4 × 4 = 64, so ∛64 = 4.

Example 2: Negative Number

Find the cube root of -27.

Solution: -3 × -3 × -3 = -27, so ∛(-27) = -3.

Example 3: Fractional Result

Find the cube root of 125.

Solution: 5 × 5 × 5 = 125, so ∛125 = 5.

FAQ

What is the difference between square root and cube root?: The square root of a number x is a number y such that y × y = x. The cube root is a number y such that y × y × y = x. Cube roots exist for all real numbers, while square roots only exist for non-negative real numbers.
Can I find the cube root of a negative number?: Yes, the cube root of a negative number is negative. For example, the cube root of -27 is -3 because (-3) × (-3) × (-3) = -27.
How accurate is the cube root calculator?: This calculator uses JavaScript's built-in Math.cbrt() function, which provides accurate results to within the limits of floating-point precision in JavaScript.
What happens if I enter a very large number?: The calculator will still compute the cube root, but very large numbers may result in scientific notation or loss of precision due to JavaScript's number representation.
Can I use this calculator for complex numbers?: No, this calculator only works with real numbers. For complex numbers, you would need a more advanced mathematical tool.