Mathematics Form 1-4 : CHAPTER TWENTY FOUR – CUBES AND CUBE ROOTS

Specific Objectives

By the end of the topic the learner should be able to:

• Find the cube of a number by multiplication
• Find the cube root of a number by factor method
• Find cubes of numbers from mathematical tables
• Evaluate expressions involving cubes and cube roots
• Apply the knowledge of cubes and cube roots to real life situations

Content

1. Cubes of numbers by multiplication.
2. Cube roots of numbers by factor method.
3. Cubes from mathematical tables.
4. Expressions involving cubes and cube roots.
5. Application of cubes and cube roots.

Introduction

Cubes

The cube of a number is simply a number multiplied by itself three times, e.g.

a × a × a = a³

1 × 1 × 1 = 1³, 8 = 2 × 2 × 2 = 2³, 27 = 3 × 3 × 3 = 3³

Example 1

What is the value of 6³?

6³ = 6 × 6 × 6

= 36 × 6

= 216

Example 2

Find the cube of 1.4

= 1.4 × 1.4 × 1.4

= 1.96 × 1.4

= 2.744

Use of tables to find roots

The cubes can be read directly from the tables just like squares and square roots.

Cube Roots using factor methods

Cubes and cube roots are opposite. The cube root of a number is the number that is multiplied by itself three times to get the given number.

Example

The cube root of 64 is written as:

64 = 4 because 4 × 4 × 4 = 64

= 3 because 3 × 3 × 3 = 27

Example

Evaluate:

= 2 × 3

= 6

Note

After grouping them into pairs of three, you choose one number from the pair and multiply.

Example

Find:

The volume of a cube is 1000 cm³. What is the length of the cube?

Volume of the cube, v = l³

l³ = 1000

l = 10

The length of the cube is therefore 10 cm.

End of topic