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How do you determine whether a number is a LEARNING
perfect cube? STANDARDS
Determine whether
We can also use the method of prime factorisation to determine a number is a
whether a number is a perfect cube. In this method, if the perfect cube.
prime factors can be grouped into three identical groups, then
the number is a perfect cube.
CHAPTER
3
9

Determine whether each of the following numbers is a
perfect cube. Perfect cube can be
written as a product of
(a) 64 (b) 240 three equal factors.
For example,
64 = 4 × 4 × 4
(a) 64 is a perfect cube.
64
8 8
4 2 4 2

2 2 2 2 2 2 Think Smart

These prime factors This number is a perfect
64 = 2 × 2 × 2 × 2 × 2 × 2 can be grouped into square and also a perfect
three identical groups. cube. What is this number?
Thus, 64 is a perfect cube.

(b)
240
12 20

3 4 4 5

3 2 2 2 2 5 These prime Discuss why the prime
factors cannot be factors of a perfect cube
240 = 3 × 2 × 2 × 2 × 2 × 5 must be grouped into
grouped into three
identical groups. three identical groups.
Thus, 240 is not a perfect cube.

Self Practice 3.2a

1. By using the prime factorisation method, determine whether each of the following
numbers is a perfect cube.
(a) 27 (b) 45 (c) 215 (d) 343

60
Chapter 3

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