Cambridge International Mathematics

Exponents and surds (Chapter 6) 139

2 Simplify:

a 3

p

3 £ 2

p

2 b 2

p

3 £ 3

p

5 c

p

2 £

p

3 £

p

5

d

p

3 £

p

2 £ 2

p

2 e ¡ 3

p

2 £(

p

2)^3 f (3

p

2)^3 £(

p

3)^3

3 Simplify:

a

p

8

p

2

b

p

2

p

8

c

p

18

p

2

d

p

2

p

18

e

p

20

p

5

f

p

5

p

20

g

p

27

p

3

h

p

18

p

3

i

p

3

p

30

j

p

50

p

2

k

2

p

6

p

24

l

5

p

75

p

3

4 Write the following in the form k

p

2 :

a

p

8 b

p

18 c

p

50 d

p

98

e

p

200 f

p

288 g

p

20 000 h

q

1

2

5 Write the following in the form k

p

3 :

a

p

12 b

p

27 c

p

75 d

q

1

3

6 Write the following in the form k

p

5 :

a

p

20 b

p

45 c

p

125 d

q

1

5

7aFind:

i

p

16 +

p

9 ii

p

16 + 9 iii

p

25 ¡

p

9 iv

p

25 ¡ 9

b Copy and complete: In general,

p

a+b 6 =:::::: and

p

a¡b 6 =::::::

8 Write the following in simplest surd form:

a

p

24 b

p

50 c

p

54 d

p

40 e

p

56 f

p

63

g

p

52 h

p

44 i

p

60 j

p

90 k

p

96 l

p

68

m

p

175 n

p

162 o

p

128 p

p

700

9 Write the following in simplest surd form:

a

q

5

9 b

q

18

4 c

q

12

16 d

q

75

36

The rules for expanding brackets involving surds are identical to those for ordinary algebra.

We can thus use:

a(b+c)=ab+ac

(a+b)(c+d)=ac+ad+bc+bd

(a+b)^2 =a^2 +2ab+b^2

(a¡b)^2 =a^2 ¡ 2 ab+b^2

(a+b)(a¡b)=a^2 ¡b^2

G MULTIPLICATION OF SURDS [1.10]

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