Cambridge International Mathematics

138 Exponents and surds (Chapter 6)

Example 19 Self Tutor

Simplify: a

p

32

p

2

b

p

12

2

p

3

a

p

32

p

2

=

q

32

2

=

p

16

=4

b

p

12

2

p

3

=^12

q

12

3 fusing

p

a

p

b

=

r

a

b

g

=^12

p

4

=^12 £ 2

=1

Example 20 Self Tutor

Write

p

32 in the form k

p

2.

p

32

=

p

16 £ 2

=

p

16 £

p

2 fusing

p

ab=

p

a£

p

bg

=4

p

2

SIMPLEST SURD FORM

A surd is insimplest formwhen the number under the radical sign is the smallest

integer possible.

Example 21 Self Tutor

Write

p

28 in simplest surd form.

p

28

=

p

4 £ 7 f 4 is the largest perfect square factor of 28 g

=

p

4 £

p

7

=2

p

7

EXERCISE 6F

1 Simplify:

a

p

2 £

p

5 b

p

3 £

p

7 c

p

3 £

p

11

d

p

7 £

p

7 e

p

3 £ 2

p

3 f 2

p

2 £

p

5

Look for the

largest perfect

square factor.

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