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Cube Root Calculator
Calculate a cube root, simplify it by pulling out perfect cubes, and see a decimal rounded to eight significant figures.
A whole number or a decimal. Negatives are allowed, and the cube root of −8 is −2.
Examples
Enter a radicand to see the cube root.
Enter a radicand to see the cube root.
Perfect cubes from 1³ to 12³. Choose a row to use that cube as the radicand.
This cube root calculator is for algebra class and homework that asks for ∛x. Enter a radicand and the page shows the cube root. Whole numbers are reduced by pulling out groups of three equal prime factors, so the cube root of 216 is 6 and ∛16 = 2∛2. A negative radicand stays negative, so the cube root of −8 is −2. When the root is not a whole number, the decimal is rounded to eight significant figures.
Perfect cubes to know
A cube root undoes cubing. The cube root of a number x is the number y such that y × y × y = x, written ∛x. A perfect cube is an integer raised to the third power. The ones that come up constantly are 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, and 10³ = 1000. So the cube root of 8 is 2, the cube root of 27 is 3, the cube root of 64 is 4, the cube root of 125 is 5, the cube root of 216 is 6, and the cube root of 1000 is 10.
Simplifying a cube root
A cube root is simplified when the number under the radical has no perfect-cube factor other than 1. Factor the radicand into primes and pull out groups of three equal factors. 16 = 2⁴ = 8 × 2, and the cube root of 8 is 2, so ∛16 = 2∛2. The 2 that is left stays under the radical. 216 = 2³ × 3³, so both groups come out and ∛216 = 2 × 3 = 6. If no factor repeats three times, as with ∛2 or ∛12, the radical is already simplified. The calculator then shows a decimal instead of pretending the root is a whole number.
Negative numbers and decimals
Unlike a square root, the cube root of a negative number is real and negative, because a negative multiplied by itself three times is still negative. (−2) × (−2) × (−2) = −8, so ∛−8 = −2. The same sign rule applies after simplifying: ∛−16 = −2∛2. A decimal radicand, or a whole number that is not a perfect cube, is shown as a decimal. When that decimal is rounded, the page says it is rounded to 8 significant figures and uses ≈. An exact whole-number result uses =, as in ∛64 = 4.
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Frequently Asked Questions
What is the cube root of 64?
The cube root of 64 is 4, because 4 × 4 × 4 = 64. 64 is a perfect cube, 4³, and its prime factorization is 2⁶, which is (2²)³.
What is the cube root of 216?
The cube root of 216 is 6, because 6 × 6 × 6 = 216. 216 = 2³ × 3³, so ∛216 = 2 × 3 = 6.
What is the cube root of 27?
The cube root of 27 is 3, because 3 × 3 × 3 = 27. 27 is 3³, a perfect cube.
What is the cube root of 8 and the cube root of 1000?
The cube root of 8 is 2, because 2 × 2 × 2 = 8. The cube root of 1000 is 10, because 10 × 10 × 10 = 1000. 1000 = 10³ = 2³ × 5³.
What is the cube root of a negative number, and how do you simplify ∛16?
The cube root of a negative number is negative. ∛−8 = −2, since (−2)³ = −8. To simplify ∛16, write 16 as 8 × 2. The cube root of 8 is 2, so ∛16 = 2∛2, which is about 2.5198421.