STRAND: Number
TOPIC:
Whole numbers
Order of operations with
squares and square roots
When evaluating expressions containing more than one operation, the following order must be observed:
1. brackets
2. squares and square roots
3. multiplication and division
4. addition and subtraction.
Operations that are equally important must be performed in order of occurrence (that is, from left to right). For example, if
division comes before multiplication, division has to be done first.
WORKED Example
Evaluate each of the following.
a 36 − 22
b 25 + 42 ÷ 8
THINK
WRITE
a
Copy down the question.
Square and roots have to be done before
subtraction, in order from left to right. So
calculate the square root of 36 first.
Square the 2 (that is, multiply 2 by itself).
Subtract.
a
Copy down the question.
Squares and roots have to be done first in
order from left to right, so calculate the
square root of 25 first.
Square the 4 (that is, multiply it by itself).
Division has to be done before addition.
Add 5 and 2 to complete the calculations.
b
1
2
3
4
b
1
2
3
4
5
36 − 22
= 6 − 22
=6−4
=2
25 + 42 ÷ 8
= 5 + 42 ÷ 8
= 5 + 16 ÷ 8
=5+2
=7
Try these
1 22 +
16
5
25 − 22
9
36 × 22 + 82
2 82 −
49
6 22 × 32 ÷ 22
10 32 ×
36 × 42
3 32 + 42 − 22
4
7 52 ×
8 42 ÷
9 − 32
11 72 − 42 ÷
4 +
25
12
36 × 22
64 − 2
36 × 32 −
16 ÷ 22
 John Wiley & Sons Australia, Ltd 2001