Page 111 - Mathematics_Form_Two

Exponents and radicals

they process two batches of plastic Solution
waste. The first batch can be (a) 3× 5 = 15
processed at a rate of 3 81 tons per
day, while the second batch can be (b) Given that 2× 32, it follows,

processed at a rate of 2 24 tons 32 = 22222´´´´
3
per day. What is the total amount
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of plastic waste processed per day = 42
when the two batches are combined? Thus, 2´ 32´ 2´ 32 32 =2 4 2= 2 4 2= ´ ´ 2 4 2´
2
Simplify your answer. = 14 2 ´ 2 2
=
=
= 14´´ 2´´
14´´ 2 ´ 2´
4. A hospital is studying two new = 14´´
= 14´´
=
14 2´´ 2 2
medications, each with a different = 8 Mathematics for Secondary Schools
= 8 8
absorption rate in the body. The = = = 8
absorption rate for the first medication
is 80 mg/hour, and for the second (c) Given 20× 28, it follows that,
4
4
medication, it is 35 mg/hour. 20 = 2 2 5 2´´ = 5
What is the difference in absorption
rates between the two medications? 28 = 2 2 7 2´´ = 7
Simplify your answer.
Thus, 20´ 28 2 5 2 7
=
´
Thus, 20´
´
28 2 5 2 7
=
7
22
22
= ´´
Multiplication of radicals = ´´ 5´ 5´ 7
´
Multiplication of radicals involves = 4´ = 57 57
4´
´
multiplying the numbers inside the
=
radicals and then simplifying if possible. = 4 35 4 35
Thus, when multiplying radicals, the
indices must be the same. Otherwise, it is (d) 1 2 ( 3 5 + ) 4= 3 ´ ( 3 5 + )
impossible.
Generally, n a ´ n b = n ab = 2 3 ( 3+ 5 )

Example 5�32 23= ´ 3 + 23 ´ 5
Simplify each of the following = 2 3 2 15= ´ + 3 2 15= 2´ +
expression products:

(a) 3 5´ (b) 2´ 32 = 6 2 15+

(e) Given 2 3 − ( 2 × ) ( 3 3 2+ )
(c) 20´ 28 (d) 12 ( 3 + 5 )

Expand as follows;
(e) ( 2 3− 2 × 3+3 2 ) ( 23 - 2 ´ ) ( 3 32 = 23´ 3 + 23 32 + - ) ( 2 ´ 3 + - ) ( 2 32 )
) (
) (
) (
´
´
+
-
= 29 6 6 - 6 34
+
23 5 6 32
105 = ´ + -´
Student's Book Form Two
6 56 6
=+ -
665 6
= - +
MATHEMATIC F2 v5.indd 105
11/10/2024 20:12:30
MATHEMATIC F2 v5.indd 105 11/10/2024 20:12:30
= 56