Skip to content
QuickToolio
esEspañolenEnglishptPortuguêsfrFrançaisdeDeutschitItaliano

Root calculator: square, cube and any index

Calculate the root of a number with any index you like. It defaults to the square root (index 2); change the index to 3 for the cube root, 4 for the fourth root, and so on.

Processed on your device. Nothing is sent to any server.

Square root

4

Raises the radicand to 1/n, which is the definition of the root of index n:

  • ⁿ√x = x^(1/n)
  • Examples: √16 = 4; ∛27 = 3; ⁴√81 = 3; ∛−8 = −2

Use cases

  • Solving math exercises with roots of any index.
  • Finding the side of a square or cube from its area or volume.
  • Getting the average growth rate over several periods (nth root of total growth).

How it works

  1. 1

    Type the radicand

    The number you want the root of. Decimals and negatives are accepted.

  2. 2

    Change the index if needed

    Leave it at 2 for the square root or type another index; the result updates instantly.

Technical details

  • With an odd index the radicand can be negative, and so is the result (∛−8 = −2).
  • With an even index and a negative radicand there's no real root (it would be a complex number): the calculator shows "-".
  • Index 0 is meaningless (it would divide by 0) and also shows "-". Decimal and negative indices are accepted: ⁻²√4 = 4^(−1/2) = 0.5.
  • Result with up to 10 significant digits.

Frequently asked questions

Why is the square root of 16 just 4 and not also −4?

Both square to 16, but the √ symbol denotes the principal root by convention, which is the positive one. If you're solving an equation like x² = 16, the solutions are ±4.

How do I get a cube root?

Type the number as the radicand and set the index to 3.

Related tools

← Calculators