Cambridge Additional Mathematics

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Surds, indices, and exponentials (Chapter 4) 103

EXERCISE 4A.1


1 Write as a single surd or rational number:
a

p
11 £

p
11 b

p
3 £

p
5 c (

p
3)^2 d

p
5 £

p
6
e 2

p
2 £

p
2 f 3

p
2 £ 2

p
2 g 3

p
7 £ 2

p
7 h (3

p
5)^2

i

p
12
p
2

j

p
18
p
3

k

p
20
p
5

l

p
6 £

p
10
p
12

Example 2 Self Tutor


Write

p
18 in the form a

p
b whereaandbare integers andais as large as possible.

p
18
=

p
9 £ 2 f 9 is the largest perfect square factor of 18 g
=

p
9 £

p
2
=3

p
2

2 Write in the form a

p
b whereaandbare integers andais as large as possible:
a

p
8 b

p
12 c

p
20 d

p
32
e

p
27 f

p
45 g

p
48 h

p
54
i

p
50 j

p
80 k

p
96 l

p
108

OPERATING WITH SURDS


The rules for adding, subtracting, and multiplying by surds are the same as those for ordinary algebra.

Example 3 Self Tutor


Simplify: a 3

p
3+5

p
3 b 2

p
2 ¡ 5

p
2

a 3

p
3+5

p
3
=8

p
3

b 2

p
2 ¡ 5

p
2
=¡ 3

p
2

Example 4 Self Tutor


Simplify:
a

p
5(6¡

p
5) b (6 +

p
3)(1 + 2

p
3)

ab(6 +

p
3)(1 + 2

p
3)
= 6 + 6(2

p
3) +

p
3(1) +

p
3(2

p
3)
=6+12

p
3+

p
3+6
=12+13

p
3

In , compare with
25=3xx x¡¡

b

p
5(6¡

p
5)
=

p
5 £6+

p
5 £¡

p
5
=6

p
5 ¡ 5

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Y:\HAESE\CAM4037\CamAdd_04\103CamAdd_04.cdr Thursday, 3 April 2014 5:04:33 PM BRIAN

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