Cube root (∛x)

Calculate the cube root of a number, including negatives.

Graf funkce

Co je cube root

The cube root ∛x is the inverse of cubing – it finds the number which, when cubed, gives x. For example ∛27 = 3, because 3³ = 27.

Where it is used in practice

  • Finding the edge of a cube from its volume.
  • Scaling – from a ratio of volumes find the ratio of dimensions.
  • Physics and chemistry when working with volumetric quantities.

Good to know

The cube root also works for negative numbers: ∛(−8) = −2, because (−2)³ = −8.

Rules of exponents

When working with powers it helps to know the basic rules, which always hold:

xⁿ · xᵖ = xⁿ⁺ᵖ   (product – add the exponents)
xⁿ ÷ xᵖ = xⁿ⁻ᵖ   (quotient – subtract the exponents)
(xⁿ)ᵖ = xⁿ·ᵖ   (power of a power – multiply)
x⁻ⁿ = 1 / xⁿ   (negative exponent)
x^(1/n) = ⁿ√x   (root as a power)

In detail with examples: rules of exponents.

Tip: very large numbers are shown in shortened form – use scientific notation.