Free · Powers and roots
Perfect Cube Integer Check
Check whether a signed number is the cube of an integer, with the exact multiplication shown for valid cubes.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
−64 is a perfect cube because (−4)×(−4)×(−4)=−64.
A number n is a perfect cube exactly when n=k³ for an integer k.
Worked example
Enter these known values and leave the other values blank.
- Number
- -64
- Result
- -64 is a perfect cube. Its signed integer cube root is -4.
- Explanation
- -64 = (-4) × (-4) × (-4)
- Explanation
- The cube root of -64 is -4.
Assumptions and limitations
- Perfect cube means an integer multiplied by itself three times. Zero is a perfect cube; a negative integer cube has a negative cube root.
- The absolute input must be below10^50 for the reviewed exact candidate comparison. Larger inputs are rejected with an explanation; this is a numerical verification budget, not a mathematical bound.
- Decimal nonintegers are not integer cubes. The hidden approximate cube root remains available to the retained calculation; only verified integer roots appear in the worked explanation.
- Every captured explanation branch and the single number control are retained. Clear removes the outcome; reset restores a blank number. Finite values too small for fixed decimal display use scientific notation.
Common questions
Is zero a perfect cube?
Yes:0×0×0=0.
Can a negative number be a perfect cube?
Yes. For example,(−4)³=−64.
Which number expressions can I enter?
Enter a finite decimal or scientific-notation number. Exact finite-decimal arithmetic such as 1/8 or 1−1 is supported. Repeating fractions such as 1/3, expressions that lose digits, functions, symbols and other bases are held; enter a decimal value instead. Computational proof limits are stated in the reference note. The ambiguous expression 0^0 is rejected.
References
Classify integer cubes by an exact cubed candidate comparison in the reviewed |input|<10^50 range, rather than checking whether an approximate cube root happens to be an integer. Preserve negative/zero cases and exact integer-root explanations. The absolute input must be below10^50, so the cubed integer candidate stays within the64-significant-digit arithmetic budget. This is a computational verification limit, not a mathematical limit on perfect cubes. Finite tiny noninteger inputs retain scientific display when fixed decimal formatting cannot preserve them. Inputs accept finite decimal/scientific literals and provably exact finite-decimal arithmetic (+, −, ×, ÷ and bounded integer powers). Lossy, repeating, function, symbolic and other-base expressions are rejected: enter a decimal value instead. The ambiguous expression 0^0 is rejected. Proof work is bounded to 20000 characters/coefficient digits, 512 nodes, depth64, 10000 aligned decimal places or absolute integer exponent, and one million Euclidean digit-work units; these are computational limits, not physical domains. Only captured editable controls are accepted as manual/API inputs.