CUBES AND CUBE ROOTS - Mathematics Form 2 Notes

• Cubes
• Use of Tables to Find Roots
• Cube Roots using Factor Methods

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?

Solution
6³ =6 x6 x 6
= 36 x 6
=216

Example 2

Find the cube of 1.4

Solution

=1.4 x 1.4 x 1.4
=1 .96 x 1 .4
=2.744

Use of Tables to Find Roots

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

Cube Roots Using Factor Methods

• Cubes and cubes 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 x 4 x 4 =64
∛27 = 3 Because 3 x 3 x 3= 27

Example

Evaluate:∛216

Solution

=∛(2 x 2 x2 x 3 x3 x3 )
=2x3
=6

Note;

• After grouping them into pairs of three you chose one number from the pair and multiply

Example

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

Solution

Volume of the cube, v = l³
L³=1 000
L =∛1000
=10
The length of the cube is therefore 10 cm