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Apka Apna Career Saathi
Apka Apna Career Saathi
Algebra Cube Roots
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Real cube root∛x
Cube root formula: ∛x = y where y³ = x
Cube Root
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∛xy³ = x
∛x
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(∛x)³
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Perfect cube
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How this cube root calculator works
Enter a number x. The calculator finds the real cube root ∛x, the number y where y³ = x. It also cubes that root again and tells you whether x is a perfect cube.
∛27 = 3 and ∛(−8) = −2. If x is not a perfect cube, the root is a decimal, such as ∛2 ≈ 1.259921.
Cube root chart
Perfect cube is Yes only for whole numbers that are exact cubes.
| x | ∛x | Perfect cube |
|---|---|---|
| 1 | 1 | Yes |
| 8 | 2 | Yes |
| 27 | 3 | Yes |
| 64 | 4 | Yes |
| 125 | 5 | Yes |
| −8 | −2 | Yes |
| 2 | 1.259921 | No |
| 0 | 0 | Yes |
How to read the result
∛x
The real cube root. For 125 it is 5. For −8 it is −2.
(∛x)³
The root cubed again. It should match the number you entered.
Perfect cube
Yes when a whole number k satisfies k³ = x. Decimals are marked No.
Negative numbers
Cube roots of negatives are allowed. Square roots of negatives are not real numbers.
Frequently asked questions
What is a cube root?
The cube root of x is the number y such that y × y × y = x. It is written ∛x. The cube root of 27 is 3, because 3³ = 27. The cube root of 8 is 2.
How does this calculator find ∛x?
Enter x. The tool returns the real cube root, then cubes that result again as (∛x)³ so you can check it matches x. For 64, ∛64 is 4 and 4³ is 64.
When does Perfect cube say Yes?
Yes only when x is a whole number and some whole number k satisfies k³ = x. 27, 8, 1, 0, and −8 are perfect cubes. 20 and 2.5 are not.
Can a negative number have a cube root?
Yes. Unlike a square root, a real cube root of a negative number exists. ∛(−8) = −2, because (−2)³ = −8. The sign stays negative.
Why is the cube root of 2 not a whole number?
2 is not a perfect cube. ∛2 is about 1.259921. Cubing that value returns 2, and Perfect cube stays No because no whole number cubes to 2.
What is the circle showing?
The ring is a visual scale of the cube root, filled at 10. A cube root of 10, which is ∛1000, fills the circle. The number result itself is not limited to 10.
Decimal roots are rounded for display. Cube the shown root if you need to confirm it returns your original number.