Indices, Standard Form And Surds Worksheet Page 11
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17Chapter 25 Indices, standard form and surds
Exercise 25H
B
Work out the value of the following.
1
_
1
_
1
_
1
_
1
(
)
_
_
1
1
a
9
b
4 9
c
10 0
d
4
e
2
2
2
2
2
4
Work out the value of
2
_
_
_
1
1
_
1
(
)
_
1
_
1
1
a
2 7
b
100 0
c
(64 )
d
12 5
e
3
3
3
3
3
8
Work out the value of
3
_
_
_
_
_
1
1
1
(
)
1
(
)
1
__
_
1
4
16
4
125
a
b
c
d
e
4
2
3
5
2
32
9
A
Work out the value of
4
_
_
_
_
2
2
2
_
3
3
a
2 7
b
100 0
c
6 4
d
1 6
e
2 5
3
3
3
4
2
Work out, as a single fraction, the value of
5
_
_
_
2
_
3
1
2
3
_
125
10 000
27
8
64
a
b
c
d
e
3
4
3
3
2
_
(
_
(
2
)
1
)
_
2
_
2
1
2
f
12 5
g
8
3
3
5
5
A
Find the value of n.
6
__
__
_
__
1
1
3
a
8
b
64 2
c
5
d
(
7 )
5
7
e
(
2 )
11
2
n
n
n
n
√
n
√
__
8
5
√
25.4
Using surds
Why do this?
Objectives
__
_____
1
5
√
Surds occur in nature. The golden ratio
You can simplify surds.
2
occurs in the arrangement of branches along the
You can expand expressions involving surds.
stems of plants, as well as veins and nerves in
You can rationalise the denominator of a fraction.
animal skeletons.
Get Ready
1. Write down the fi rst 10 square numbers.
__
___
2. Write down the value of
a
36
b
100
√
√
__
__
__
__
3. Which of these has an exact answer:
5 ,
9 ,
37 ,
64 ?
√
√
√
√
Key Points
A number written exactly using square roots is called a surd.
__
__
2 and
3 are both surds.
√
√
__
__
2
3 and 5
2 are examples of numbers in surd form.
√
√
__
__
4 is not a surd as
4 2.
√
√
These two laws can be used to simplify surds.
__
__
m
__
__
___
√
___
m
__
m
n
mn
√
√
√
√
__
n
n
√
Simplifi ed surds should never have a surd in the denominator.
620
surd
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