Surds And Indices Page 14
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28Multiplication of surds
F
__
__
x ×
x = x
Surds can be multiplied using the properties
√
√
__
__
__
x ×
y =
and
xy .
√
√
√
EXAMPLE 1
Simplify the following.
__
__
__
__
__
__
__
4 × 3
5 × 2
2 × 3
8 × 4
√
√
√
√
√
√
√
a
b
c
d
7
3
3
6
8
5
3
__
__
__
__
__
__
4 × 3
7 = 4 × 3 ×
5 × 2
3 = (2 × 3) × (
5 ×
√
√
√
√
√
√
a
b
7
3
3 )
___
__
= 12
= 6
√
√
7
15
__
__
__
__
__
__
__
__
2 × 3
8 = (6 × 3) × (
2 ×
8 × 4
3 = (5 × 4) × (
8 ×
√
√
√
√
√
√
√
√
c
d
6
8 )
5
3 )
___
___
= 18 ×
= 20 ×
√
√
16
24
__
__
= 18 × 4
= 20 ×
4 ×
√
√
6
__
= 72
= 20 × 2
√
6
__
= 40
√
6
Exercise 11F
1
Simplify the following.
__
__
__
5 × 2
2 × 6
7 × 10
√
√
√
a
b
c
3
2
4
__
__
__
__
__
__
3 × 6
5 × 3
7 × 7
√
√
√
√
√
√
d
e
f
3
2
10
7
6
6
__
___
___
__
__
___
2 × 3
32 × 5
5 × 3
√
√
√
√
√
√
g
h
i
6
18
2
2
20
__
__
__
__
___
__
3 × 2
6 × 2
10 ×
√
√
√
√
√
√
j
k
l
5
8
6
2
3
2
EXAMPLE 2
Simplify the following.
__
__
__
__
__
__
__
__
7 + 2
7 − 3
5 + 3
√
√
√
√
√
√
√
√
a
b
c
3(
6 )
2 (
5 )
4
3 (2
2 )
__
__
__
__
7 + 2
6 ) = 3 ×
7 + 3 × 2
√
√
√
√
a
3(
6
__
__
= 3
7 + 6
√
√
6
__
__
__
__
__
__
__
Use the distributive law to remove
7 − 3
5 ) =
2 ×
7 +
2 × (−3
√
√
√
√
√
√
√
b
2 (
5 )
grouping symbols: a(b + c) = ab + ac
___
___
=
14 − 3
√
√
10
__
__
__
__
__
__
__
5 + 3
2 ) = 4
3 × 2
5 + 4
3 × 3
√
√
√
√
√
√
√
c
4
3 (2
2
___
__
= 8
15 + 12
√
√
6
2
Simplify the following.
__
__
__
__
___
__
6 +
5 + 4
10 − 3
√
√
√
√
√
√
a
b
c
5(
3 )
2(
3 )
4(2
2 )
__
__
__
__
__
__
__
__
__
5 +
6 − 4
5 + 2
√
√
√
√
√
√
√
√
√
d
e
f
3 (
2 )
5 (
3 )
2 (3
7 )
___
__
___
__
__
__
__
__
__
2 − 3
5 − 2
3 + 2
√
√
√
√
√
√
√
√
√
g
h
i
2
10 (6
10 )
5
2 (3
6)
3
6 (4
8 )
14
Insight Maths 9
Australian Curriculum
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