Cambridge Additional Mathematics

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

4037 Cambridge

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