Factors and Multiples
(Cubes and Cube Roots)
Name:
(
)
Worksheet
9
Class:
Points to Note:
Cubes are the opposite of Cube Roots
Example:
The cube of 3
= 3×3×3
= 27
The cube root of 27
When the number 3 is given
I need to produce an answer
of 27.
3
=
=
27
3
When the number 27 is given
I need to produce an answer
of 3.
Note:
The cube of (−3)
= (−3) × (−3) × (−3)
= −27
Page 37
The cube root of −27
=
=
3
−27
−3
By: Mr Wong Han Ming
Examples of cubes are
1×1×1
2×2×2
3×3×3
4×4×4
5×5×5
.
.
.
=
=
=
=
=
1
8
27
64
125
.
.
.
These numbers 1, 8, 27, 64, 125, 216, …
are known as PERFECT CUBES
Example:
Find the cube root of 1 728.
Method 1:
Step 1:
Factorise the number into prime factors.
Therefore,
3
Step 2:
1 728 =
3
2 6 × 33
3
2 6 × 33
Divide into three groups.
3
1 728 =
=
3
(22 × 3) × (22 × 3) × (22 × 3)
Page 38
By: Mr Wong Han Ming
Step 3:
Taking cube root will leave with only one of the groups.
3
1 728 =
=
3
3
2 6 × 33
(22 × 3) × (22 × 3) × (22 × 3)
=
(22 × 3)
=
12
Method 2:
Step 1:
Use continuous division to reduce the
number into prime numbers.
2
2
2
2
2
2
3
3
3
1 728
864
432
216
108
54
27
9
3
1
Step 2:
From the left column, group three of the
SAME numbers together and combine
into one number.
2
2
2
2
2
2
3
3
3
1 728
864
432
216
108
54
27
9
3
1
2
2
3
Page 39
By: Mr Wong Han Ming
Step 3:
Multiply the combined numbers to get
the cube root of the given number.
3
1 728 = 2 × 2 × 3
= 12
Practice:
1)
Find the cube root of 64 using prime factorisation.
2)
Find the cube root of −343 using prime factorisation.
Page 40
By: Mr Wong Han Ming
3)
Find the cube root of 216 using prime factorisation.
4)
Find the cube root of −512 using prime factorisation.
5)
Find the cube root of 1331 using prime factorisation.
Page 41
By: Mr Wong Han Ming
6)
Find the cube root of 9261 using prime factorisation.
7)
Given that the product of 1764 and another number, k , is a perfect
cube. Find the smallest possible value of k .
8)
A cube has a volume of 46 656 cm3. Find the length of one side of the
cube.
Page 42
By: Mr Wong Han Ming
Answers:
1)
2)
3)
4)
5)
6)
7)
8)
4
−7
6
−8
11
21
42
36 cm
Page 43
By: Mr Wong Han Ming