Ctrl+k

Represent perfect cubes

A perfect cube is a whole number expressible as n×n×n=n3n \times n \times n = n^3 for a whole-number base nn, including 0; it can be represented as a three-dimensional arrangement of nn by nn by nn unit cubes. This connects repeated multiplication, exponent notation, and volume, while distinguishing cube numbers such as 8, 27, 64, and 125 from numbers that are merely divisible by 3. Negative cubes and general real cube roots are outside this scope.

Detailed Explanation: Represent perfect cubes

A perfect cube is a whole number that can be written as the same whole number multiplied by itself three times:

n×n×n=n3n \times n \times n = n^3

It can also represent the number of unit cubes in a solid that is nn cubes long, nn cubes wide, and nn cubes high.

Example: Represent (27)(27) as a perfect cube.

  1. Find a whole number that can be used three times as a factor:

3×3×3=273 \times 3 \times 3 = 27

  1. Write the repeated multiplication using an exponent:

33=273^3 = 27

  1. Interpret the representation as a three-dimensional arrangement. A solid that is 33 unit cubes long, 33 unit cubes wide, and 33 unit cubes high contains:

3×3×3=273 \times 3 \times 3 = 27

Therefore, (27)(27) is a perfect cube, represented by (33)(3^3) or a (3×3×3)(3 \times 3 \times 3) arrangement of unit cubes. A number must have the same whole-number factor repeated three times; simply being divisible by 33 is not enough.

Learn by doing: Represent perfect cubes

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Radicals - Simplifying, Cube - Values only, Nothing Remaining

      ?