Page 109 - Mathematics_Form_Two

Exponents and radicals

3. Consider the like terms and express
(g) 3 2000 (h) 2000
each term as a sum of its roots.
(i) 6 1000000 4. For each group of like terms add the
values obtained in task 3.

3. Express each of the following 5. Pick any two terms of unlike
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numbers under a single radical sign: radicals and try to add them as in
task 4. What can you conclude?
(a) 52 (b) 4 11
6. Provide the condition for radicals to
(c) 3 10 (d) 9 3 be added together. Mathematics for Secondary Schools
8

(e) 52 (f) 33
3
3
Example 5�30
(g) 2 − 1000 (h) 64 Simplify each of the following
7
4
expressions:
(i) 75
5
(a) 2 + 2 = 12 12+ = (b) 2 3 =
2 2 33 5 3+
Addition and subtraction of radicals (c) 2 81= 3 + 3 24 (d) 4 2 + 4 32
Two or more radicals can be added or
subtracted if they are alike. Radicals Solution
which are alike are those with the same (a) 2 + 2 = 12 12+ = 2 2
indices and radicand. This means that
radicals of the same index can be added or (b) 2 3 33 5 3+ =
subtracted, just as it is done in algebraic
expressions. The radicals 2 and 3 2 (c) 3 3
cannot be added or subtracted because = 2 81 + 24
3
have unlike indices. Before adding or = 2 3333××× + 3 2 2 2 3× × ×
subtracting radicals, first simplify the = 2× 3 333×× × 3 3 + 3 2 2 2× × × 3 3
terms if possible. Engage in Activity 5.4
to explore about addition and subtraction = 2 33 2 3× 3 + 3
of radicals = 83
3

Activity 5�4: Deduce the conditions (d) 4 2 + 4 32
for adding and = 4 2 + 4 2222××× × 4 2
subtracting radicals
1. Simplify the following radicals: 8 , = 4 22+× 4 2

32, 27, and 32 2 . = 4 2 22+ 4

2. Identify the like terms in task 1. = 3 2
4

103
Student's Book Form Two

11/10/2024 20:12:28
MATHEMATIC F2 v5.indd 103
MATHEMATIC F2 v5.indd 103 11/10/2024 20:12:28