Cube Root Calculator

Calculate the cube root (√x) of any positive, negative, or decimal number instantly

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Perfect Cube

What Is a Cube Root?

A cube root is a mathematical value that, when multiplied by itself three times, produces the original number. In simple terms, if a × a × a = b, then a is the cube root of b. Cube roots are widely used in mathematics, algebra, geometry, physics, and engineering.

For example, the cube root of 8 is 2 because 2 × 2 × 2 equals 8. Similarly, the cube root of 27 is 3 because 3 × 3 × 3 equals 27. Finding cube roots is particularly helpful when solving volume equations and three-dimensional measurements.

Cube Root Formula

The mathematical formula for finding the cube root of a number is:

∛x = x^1/3

In this formula, x represents the number for which you want to find the cube root.

Examples of Cube Roots

∛8 = 2 Because 2 × 2 × 2 = 8

∛27 = 3 Because 3 × 3 × 3 = 27

∛64 = 4 Because 4 × 4 × 4 = 64

∛125 = 5 Because 5 × 5 × 5 = 125

∛-8 = -2 Because (-2) × (-2) × (-2) = -8

∛100 ≈ 4.6416 Non-perfect cube (Decimal)

Common Perfect Cubes Chart

A perfect cube is a number whose cube root is a whole integer. Here are the first 10 perfect cubes:

∛1 = 1

∛8 = 2

∛27 = 3

∛64 = 4

∛125 = 5

∛216 = 6

∛343 = 7

∛512 = 8

∛729 = 9

∛1000 = 10

Cube Root of Negative Numbers

Unlike square roots, negative numbers have real cube roots. When you multiply a negative number by itself three times, the result is always negative. For example, the cube root of -27 is -3 because (-3) × (-3) × (-3) = -27.

Frequently Asked Questions

The cube root of 8 is 2 because 2 × 2 × 2 equals 8.

Yes! Negative numbers have real cube roots. For instance, the cube root of -64 is -4.

The standard formula is ∛x = x^(1/3), where x is your input number.

Since 100 is not a perfect cube, its cube root is an irrational decimal number, approximately 4.6415888336.