Page 116 - Mathematics_Form_Two

Exponents and radicals
1 = 1 ´ a b + = a b +

b -
Similarly, for 1 , the rationalizing factor is a- = 1 a ´ b a a b + = a b + b+ . ab-
a b - a b - a b+ ab-
Thus, .

Therefore, .
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Mathematics for Secondary Schools factors: a Rationalizing factor a a ´ Reason
The following table gives some options and reasons for choosing the rationalising

Denominator

a =
a
)
a
a =
a
)
)(
a
ab-
a + ab a - b a a + ab a - b ( ( a - b )( a + b a = ab-
a + b
a - b
Example 5�36
1 1 5 3 +
Rationalize the denominator in each of 1 5 1 3 - = 5 5 3 - 3 + ´ 5 3 +
the following expressions: (b) 5 1 = 5 1 ´ 5 5 3 + 5 3 +
3 +
3 1 3 - = 1 3 - ´ = 1 5 = ´ 5 3 +
(a) (b) 5 3 - 5 3 - 5 3 +( 5 3 + 3 - ) 5 3 +
5
5 5 3 - = 5 = ( 3 - 5 5 + 3 3 - 5 3 +
3 +
3 -
5
5
(
=
5 2 3+ ( 5− 3 )( = ) 5 5 + 3 3 + 5 3 + ) 3 +
(c) (d) 5 3 - = ) 5 5 3 3 +
5 + 3 2 5 - 5 3 + ( 5 - 3 - ) 5 3 +
6 = 5 5 3 3 + 5 3 +
-
(e) = = 5 3 +
2
-
72− 5 3 = 5 3
3 +
5
-
Solution = = 5 1 2 3 + 5 3 +
(a) 5 is a denominator and a single Therefore, 5 2 = 2 .

3 -
radical expression.
Multiply both numerator and (c) 5 5 5 3 -
denominator by 5 . 5 3 + = 5 3 + ´ 5 3 -
3
3 3 = = ´ ´ 5 5 5 ( 5 )
3
5 5 5 5 5 5 = 3 -
-
35 53
35
= = 5- 15
5 5 =
3 3 35 2
35
Therefore, \ \ = = .
5 5 5 5 Therefore, 5 = 5− 15 .
5 + 3 2
110
Student's Book Form Two
11/10/2024 20:12:37
MATHEMATIC F2 v5.indd 110 11/10/2024 20:12:37
MATHEMATIC F2 v5.indd 110