Perfect Cubes & Cube Roots

Front

What is a perfect cube?

Back

A perfect cube is a number that can be expressed as the cube of an integer. For example, 1, 8, 27, and 64 are perfect cubes (1³, 2³, 3³, 4³ respectively).

Front

What is the formula for the volume of a cube?

Back

The volume V of a cube with side length s is given by the formula V = s³.

Front

If the volume of a cube is 64 cubic units, what is the side length?

Back

The side length is 4 units, since 4³ = 64.

Front

What is the cube root of a number?

Back

The cube root of a number x is a value y such that y³ = x. It is denoted as ∛x.

Front

Evaluate ∛1.

Back

The cube root of 1 is 1, since 1³ = 1.

Front

What is 36 cubed?

Back

36 cubed (36³) is 46,656.

Front

Calculate ∛125.

Back

The cube root of 125 is 5, since 5³ = 125.

Front

Calculate ∛64.

Back

The cube root of 64 is 4, since 4³ = 64.

Front

What is the relationship between perfect cubes and cube roots?

Back

The cube root of a perfect cube is the integer that was cubed to obtain that number.

Front

List the first five perfect cubes.

Back

The first five perfect cubes are 1 (1³), 8 (2³), 27 (3³), 64 (4³), and 125 (5³).