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How do you determine whether a number is a LEARNING
perfect square? STANDARDS
Determine whether
We can use the method of prime factorisation to determine a number is a
whether a number is a perfect square. perfect square.

In this method, if the prime factors can be grouped into
two identical groups, then the number is a perfect square.
CHAPTER
3
1

Determine whether each of the following numbers is a
perfect square.
(a) 36 (b) 54 Perfect square can be
written as a product of
two equal factors.
(a) 36 For example,
225 = 15 × 15 or 15 2
225 is a perfect square.
4 9

2 2 3 3 These prime factors
can be grouped into
36 = 2 × 3 × 2 × 3
two identical groups.
Thus, 36 is a perfect square.

(b) 54
Discuss why the prime
factors of a perfect
6 9 square must be grouped
into two identical groups.
2 3 3 3 These prime factors
cannot be grouped into
54 = 2 × 3 × 3 × 3
two identical groups.
Thus, 54 is not a perfect square.

Self Practice 3.1a

1. Determine whether each of the following numbers is a perfect square.
(a) 45 (b) 100 (c) 214 (d) 324

50
Chapter 3

03 TB Math F1.indd 50 11/10/16 12:09 PM