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