Surds And Indices Page 20
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28EXAMPLE 3
Write the following in surd form.
1 __
1 ___
a
b
k
z
5
10
1 __
1 ___
__
_
=
=
a
5
b
10
k
5
a
z
10
z
√
√
4
Write the following in surd form.
1 __
1 __
1 __
1 __
a
b
c
d
m
y
p
t
4
2
3
8
1 __
1 __
1 __
1 __
e
f
g
h
17
25
62
x
6
4
3
n
EXAMPLE 4
Evaluate the following.
1 __
1 __
a
b
25
256
2
4
___
____
1 __
1 __
=
=
√
√
4
a
b
25
25
256
256
2
4
= 5
= 4 (since 4 × 4 × 4 × 4 = 256)
5
Evaluate the following.
1 __
1 __
1 __
1 __
1 __
a
b
c
d
e
49
2
27
3
625
4
32
5
1 000 000
6
1 __
1 __
1 __
1 __
1 ___
f
g
h
i
j
8
3
121
81
64
3
1
10
2
4
EXAMPLE 5
1 __
Use your calculator to evaluate 12
correct to 2 decimal places.
5
1 __
≈ 1.64
(
)
÷
=
12
12
1
5
5
Some calculators have different keys
for these operations.
Check:
___
12 ≈ 1.64
(
)
5
√
=
□
5
12
2
x
SHIFT
6
Use your calculator to evaluate the following, correct to 2 decimal places.
1 __
1 __
1 __
1 __
1 __
a
b
c
d
e
5
2
298
41
831
3
4
5
2
6
EXAMPLE 6
Write the following in index form.
___
__
√
a
b
(
m )
3
m
3
√
___
3
1 __
1 __
__
= ( m
√
= (m
a
b
m )
3
m
3
3
(
2
)
)
√
2
1 __
1 __
× 3
3 ×
= m
= m
2
2
3 __
3 __
= m
= m
2
2
20
Insight Maths 9
Australian Curriculum
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