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
cyan magenta yellow black Additional Mathematics
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_04\103CamAdd_04.cdr Thursday, 3 April 2014 5:04:33 PM BRIAN