Page 108 - Mathematics_Form_Two

Exponents and radicals

Example 5�27 Example 5�29

5
Express 1024 in its simplest form. Express each of the following numbers
under a single radical sign:
Solution
(a) 2 3 (b) 2 4
3
Write 1024 as a product of prime
Solution
FOR ONLINE READING ONLY
factors. (a) 2 3 = 2 × 2 × 3
Mathematics for Secondary Schools Apply the fifth root on both sides to Therefore, 2 3 = 12 .
1024 = 2×2×2×2×2×2×2×2×2×2
= 12
obtain,
5
1024 =
2222222222×××××××××
5
(b)
5
2 ×
2
5
5
=
3
3
1
5
2
2
5
×
= 32
5
3
= ( ) ( ) 1 5 2 4 = 2 × 2 × 2 × 4

= 22× Therefore, 2 4 = 32 .
3
3
= 4
4
Therefore, 1024 = � Exercise 5�7
5
1. Simplify each of the following
Example 5�28 expressions:
Express each of the following numbers (a) 169 (b) 729
in its simplest form.
(c) (d)
(a) 20 (b) 3 54 4 2048 4 2500
Solution (e) 1024 (f) 3 512
(a) 20 = 2 2´´ 5
(g) 3 343 (h) 3 1000
= 22´´ 5 t 4
2 = 5´ (i) 3 729 (j) 5
81s 24
= 25 2 = 5´
Therefore, 20 = 25= . 2. Express each of the following
expressions in simplest form.
(b) = 54 = 3×3×3×2
´´´
54 =
3
333 2
3
3
3
(a) 40 (b) 250
2
´´
= 3 333´ 3 3 54 = 3 333 2
´´´

3 = 3 = 2´ 3 333´ 3 2 (c) 6 1024 (d) 3 54
´´
3
= 3 2 3 = 3 2´ (e) 3 270 (f) 3 162
3
3
Therefore, 54 3 2
=
102
Student's Book Form Two
11/10/2024 20:12:27
MATHEMATIC F2 v5.indd 102 11/10/2024 20:12:27
MATHEMATIC F2 v5.indd 102