Page 113 - Mathematics_Form_Two

Exponents and radicals

27. Juma has a square garden of length
8.m m. What is the perimeter and the Generally, a = a where a and b are

b
total area of the garden? positive numbers. b
28. A rectangular prism has dimensions
3 metres, 6 metres, and 2 Example 5�33
metres. What is the volume of the
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prism? Express the following radicals in their
29. The length of a rectangular farm most simplified form: 18
÷
75
is 8000 metres and its width is (a) 75 ÷ 12÷ 12 (b) 5 50
2000 metres. Find the diagonal 65 23´ Mathematics for Secondary Schools
and the area of the farm. (c)
20 3 21´ 12
30. The side of a square is scaled by a
factor of 3 . If the original side Solution
length was 5 metres, what is the (a) 75 ÷ ÷ 12÷ 12 = = 75 75
75
new area of the square? 12 12
75
=
Division of radicals 12
Two radicals can be expressed as a = 3+ 25
fraction by writing one as the divisor 3+ 4
and the other as the dividend. If two or
more numbers under radicals have the = 25
same index, combine them under a single 4
radical, then divide and simplify where 5
possible. Engage in Activity 5.5 to learn = 2
more on division of radicals. 5
75
Therefore, 75 ÷ ÷ 12÷ 12 = .
2
Activity 5�5: Deducing conditions for (b)
dividing radicals 5 18 = ´ 18
5
1. In pairs, follow the steps given to 50 50
divide 20 by 5. = 5´ 18

2. Express 20 ÷ 5. as a ratio of 50
numerator and denominator. 3 2
3. Express the numerator and = 5´ 5 2
denominator in simple terms.
4. Collect together the terms with the = 5´ 3 2´
same radicals and divide. 5 2´
=
3
5. Follow the same steps to evaluate = 3
625
625 2 25÷ ÷ 2 25÷ . Therefore, 5 18 = 3.

50
107
Student's Book Form Two

11/10/2024 20:12:33
MATHEMATIC F2 v5.indd 107
MATHEMATIC F2 v5.indd 107 11/10/2024 20:12:33