Cambridge Additional Mathematics

(singke) #1
104 Surds, indices, and exponentials (Chapter 4)

EXERCISE 4A.2


1 Simplify:
a 2

p
2+3

p
2 b 2

p
2 ¡ 3

p
2 c 5

p
5 ¡ 3

p
5 d 5

p
5+3

p
5
e 3

p
5 ¡ 5

p
5 f 7

p
3+2

p
3 g 9

p
6 ¡ 12

p
6 h

p
2+

p
2+

p
2

2 Simplify:
a

p
2(3¡

p
2) b

p
5(

p
5+1) c

p
10(3 + 2

p
10) d

p
7(3

p
7 ¡4)
e ¡

p
3(5 +

p
3) f 2

p
6(

p
6 ¡7) g ¡

p
8(

p
8 ¡5) h ¡ 3

p
2(4¡ 6

p
2)

3 Simplify:
a (5 +

p
2)(4 +

p
2) b (7 + 2

p
3)(4 +

p
3) c (9¡

p
7)(4 + 2

p
7)
d (

p
3 + 1)(2¡ 3

p
3) e (

p
8 ¡6)(2

p
8 ¡3) f (2

p
5 ¡7)(1¡ 4

p
5)

Example 5 Self Tutor


Simplify:
a (5¡

p
2)^2 b (7 + 2

p
5)(7¡ 2

p
5)

a (5¡

p
2)^2

=25¡ 10

p
2+2
=27¡ 10

p
2

b (7 + 2

p
5)(7¡ 2

p
5)
=7^2 ¡(2

p
5)^2
=49¡(4£5)
=29

4 Simplify:
a (3 +

p
2)^2 b (6¡

p
3)^2 c (

p
5+1)^2 d (

p
8 ¡3)^2
e (4 + 2

p
3)^2 f (3

p
5+1)^2 g (7¡ 2

p
10)^2 h (5

p
6 ¡4)^2

5 Simplify:
a (3 +

p
7)(3¡

p
7) b (

p
2 + 5)(

p
2 ¡5) c (4¡

p
3)(4 +

p
3)
d (2

p
2 + 1)(2

p
2 ¡1) e (4 + 3

p
8)(4¡ 3

p
8) f (9

p
3 ¡5)(9

p
3+5)

DIVISION BY SURDS


Numbers like
6
p
2

and
9
5+

p
2

involve dividing by a surd.

It is customary to ‘simplify’ these numbers by rewriting them without the surd in the denominator.

For any fraction of the form
b
p
a
, we can remove the surd from the denominator by multiplying by

p
a
p
a
.

Since

p
a
p
a
=1, this does not change the value of the fraction.

=5^2 + 2(5)(¡

p
2) + (

p
2)^2

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\104CamAdd_04.cdr Friday, 31 January 2014 11:18:18 AM BRIAN

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