Algebra Cubed - Perfect Cubes

Frequently asked questions

• What is a perfect cube?

  A perfect cube is a number that can be written as k × k × k for some whole number k. Examples are 8 (2³), 27 (3³), and 125 (5³). This calculator finds k³ for the base you enter.

• How is the cube calculated?

  The cube is k³ = k × k × k. Enter 4 and the result is 64. Enter 10 and the result is 1,000. The same multiplication is used for decimals and negative numbers.

• Why is the cube of a negative number negative?

  A negative times a negative is positive, and that positive times a negative is negative again. So (−3)³ = −27, not 27. Squaring a negative number removes the sign. Cubing it keeps the sign.

• What does Integer k mean?

  Integer k is Yes when the base is a whole number, such as 4 or −3. It is No for decimals such as 2.5. Neighbouring cubes, (k−1)³ and (k+1)³, are shown only when k is an integer.

• What are the neighbouring perfect cubes?

  For a whole number k, (k−1)³ is the perfect cube just below and (k+1)³ is the one just above. For k = 4, those are 27 and 125, with 4³ = 64 in between.

• Can I cube a decimal?

  Yes. 1.5³ = 3.375 and 0.5³ = 0.125. A decimal cube is not called a perfect cube unless the result is the cube of a whole number.