Cube Root Calculator: Find ∛x with Steps
Enter any number, positive, negative or decimal, and get its cube root instantly. You also see the simplified form (like ∛54 = 3∛2) and the working, so you can do it yourself in the exam.
Need a 4th root, 5th root or any other index? Use the Root Calculator.
What is a cube root?
The cube root of a number x is the value that, multiplied by itself three times, gives x. It is written ∛x, or as the exponent x1/3. Since 4 × 4 × 4 = 64, we get ∛64 = 4.
Cubing and taking the cube root undo each other: ∛(a³) = a.
How to find a cube root by prime factorisation
Break the number into prime factors, group them in threes, and take one factor from each group.
Example: ∛216. 216 = 2 × 2 × 2 × 3 × 3 × 3. One group of three 2s and one group of three 3s give 2 × 3 = 6.
Example: ∛54. 54 = 2 × 3 × 3 × 3. The three 3s come out as a 3, and the lone 2 stays inside the root, so ∛54 = 3∛2 (about 3.7798).
Cube roots of negative numbers
A negative number multiplied by itself three times stays negative, so a cube root can be negative: ∛(−27) = −3. This is different from square roots, which have no real value for negatives.
Estimating a cube root that is not perfect
Find the two perfect cubes on either side. For ∛50, we know 3³ = 27 and 4³ = 64, so the answer lies between 3 and 4. Since 50 is closer to 64 than to 27, it is nearer 4 (the exact value is about 3.684).
Real-life use: side of a cube from its volume
The volume of a cube is side³, so the side is the cube root of the volume. A cube-shaped tank holding 343 litres (343,000 cm³) has a side of ∛343,000 = 70 cm.
Perfect cubes from 1 to 20
| n | n³ | n | n³ | n | n³ | n | n³ |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 6 | 216 | 11 | 1331 | 16 | 4096 |
| 2 | 8 | 7 | 343 | 12 | 1728 | 17 | 4913 |
| 3 | 27 | 8 | 512 | 13 | 2197 | 18 | 5832 |
| 4 | 64 | 9 | 729 | 14 | 2744 | 19 | 6859 |
| 5 | 125 | 10 | 1000 | 15 | 3375 | 20 | 8000 |
Cube root FAQ
The cube root of x is the number that, multiplied by itself three times, gives x. It is written ∛x. For example, ∛64 = 4 because 4 × 4 × 4 = 64.
Factorise the number into primes and group them in threes. For 216 = 2³ × 3³, one 2 and one 3 come out of each group, so ∛216 = 2 × 3 = 6. For numbers that are not perfect cubes, estimate between the two nearest perfect cubes.
Yes. Unlike square roots, the cube root of a negative number is a real negative number. For example, ∛(−27) = −3 because (−3) × (−3) × (−3) = −27.
1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. These are the cubes of 1 through 10.
Write 54 as 2 × 3 × 3 × 3. The group of three 3s comes out as a single 3, and the 2 stays inside, so ∛54 = 3∛2.
The volume of a cube is side³, so the side is the cube root of the volume. A cube with volume 343 cm³ has side ∛343 = 7 cm.