Cube and Cube Roots

Cube and Cube Roots

Cube Numbers

A number obtained by multiplying any number three times is called a cube number. It is represented by giving the power 3 to the multiplicand.

For example,

Cube of 0 = 0³ = 0 × 0 × 0 = 0

Cube of 1 = 1³ = 1 × 1 × 1 = 1

Cube of 2 = 2³ = 2 × 2 × 2 = 8

Cube of 3 = 3³ = 3 × 3 × 3 = 27

Cube of 4 = 4³ = 4 × 4 × 4 = 64

Cube of 5 = 5³ = 5 × 5 × 5 = 125 and so on.

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Perfect Cube Numbers

Cube of whole numbers i.e 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, … etc are called perfect cube numbers.

Some facts of cube numbers:

1.    Cube of even positive integer is even.

2.    Cube of positive integer is a positive number.

3.    Cube of negative integer is s negative number.

4.    Cube of odd positive integer is odd.

Cube Root

Cube number and cube root are correlated. When we multiply three same numbers we get a cube number, and that multiplicand of the cube number is called a cube root. It is represented by giving power 1/3 to the cube number or using radical sign of cube root as shown below:

Cube root can be calculated by using the prime factorization methods:

In this method we factorize the number into its prime factors and form the power of 3.

For example,          

Workout Examples

Example 1: Find the cube of 11.

Solution: Here,

                        Cube of 11 = 11³ = 11 × 11 × 11 = 1331

Example 2: Find the cube root of 1728 by prime factorization method.

Solution: Here,

You can comment your questions or problems regarding the cube numbers and cube root here.