Check whether a whole number is the cube of an integer and compare it with its real cube root.
Complete the required fields and select the calculate button.
Enter a whole number. Negative perfect cubes are valid because an odd power preserves the negative sign.
A perfect cube is an integer obtained by multiplying another integer by itself three times. The number 125 is a perfect cube because 5 × 5 × 5 = 125. A negative integer can also be a perfect cube: (−5) × (−5) × (−5) = −125.
This calculator checks a whole number and reports whether it is a perfect cube. It also shows the integer root candidate, that candidate cubed, and a decimal cube-root approximation for comparison. Decimal inputs are rejected instead of being silently changed into integers.
Use a whole number without commas or a decimal point. A value such as 125.9 is not an integer and the form will ask you to correct it.
| Quantity | Explanation |
|---|---|
| n | The integer being classified. Both positive and negative whole numbers are valid mathematical candidates. |
| k | An integer root candidate. The actual test is whether cubing it reproduces n. |
| Perfect-cube verdict | A statement about the integer test. A nearby integer root does not establish that n is a perfect cube. |
For n = 216, the candidate root is 6. Cubing it gives 6 × 6 × 6 = 216, so the number is a perfect cube. For n = 217, the same nearby candidate has cube 216, not 217. The second number is therefore not a perfect cube.
For n = −343, the root candidate is −7. Cubing −7 gives −343, so the verdict is yes. Negative perfect cubes are possible because multiplying three negative factors leaves a negative result.
A cube with volume 512 cubic centimeters has edge length 8 centimeters because 8³ = 512. A volume of 500 cubic centimeters also defines a real edge length, but that edge is not a whole number. “Not a perfect cube” does not mean that no real cube root exists.
If someone suggests that 1,000 is a perfect cube with root 10, multiply 10 × 10 × 10 directly. For small integers, this exact product is clearer than deciding whether a printed decimal root looks close enough to an integer.
Perfect-cube checks help with number patterns, exact integer problems and simplifying cube roots. If a cube-root expression contains a perfect-cube factor, that factor can be taken outside the radical: ∛(8 × 3) = 2∛3. The calculator classifies one integer at a time rather than carrying out a symbolic factorization.
The sequence 0, 1, 8, 27, 64, 125 and 216 consists of the cubes of 0 through 6. The gaps grow as the roots increase. If 125 < n < 216, its positive cube root lies between 5 and 6, so there is no integer root in that open interval.
The decimal root is useful for seeing where the number lies between neighboring cubes. The verdict comes from cubing the nearby integer candidate and comparing that product with the original whole number. The form limits the accepted range so this integer check stays within dependable arithmetic.
Yes. Zero is 0³ and one is 1³. The number −1 is also a perfect cube because (−1)³ = −1. These values fit the same integer definition as larger examples.
No. Every real number has a real cube root. The perfect-cube question asks whether that root is an integer. For instance, 2 has a real cube root but is not an integer perfect cube.
The integer candidate is the nearby whole number used for the exact cube check. For a non-cube, use the separate approximate cube-root value to see the decimal result.
Yes. For example, 64 = 8² = 4³. More generally, a nonnegative integer raised to the sixth power is both a square and a cube.