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How do you determine the cube root of a number?

13 LEARNING

STANDARDS
Find the value of each of the following without using Determine the cube
a calculator. root of a number

3
3
(a) 64 (b)  without using
216
technological tools.

CHAPTER
3 ? × ? × ? = 64

3
3
(a) 64 = 4 4 × 4 × 4 = 64
 3
= 4 4 3 = 64
(b)
216
216 = 3 × 2 × 2 × 3 × 3 × 2
12 18 = (3 × 2) × (3 × 2) × (3 × 2)
= 6 × 6 × 6 Prime factorisation is a
3 4 3 6   more systematic method
3
3
216 = 6 × 6 × 6
used to find the cube
= 6 root of a larger number.
3 2 2 3 3 2

14

Find the value of each of the following without using a calculator.
8 81 3
(a) 3 (b) 3 – (c) 3 3
125 192 8
3
8
8 
(a) 3 =
8 81 125 
3
125
(a) 3 (b) 3 –
125 192 3  3
2
=
2 2 2 81 27 3  3
= 3 × × = 3 – Simplify the 5
5 5 5 192 64 fraction first. 2
=
2
1 2 3 27 5
= 3 5 = 3 – 64
2 3
1
= = 3 – 3 2
5 4
3
= –
4
3 27
(c) 3 3 = 3 Convert to improper
8 8 fraction first. The cube root of a
1 2 3 positive number is
3
= 3 always a positive value
2
3 whereas the cube root
= of a negative number is
2 always a negative value.
1
= 1
2
64
Chapter 3

03 TB Math F1.indd 64 11/10/16 12:10 PM