Addition and Subtraction of Radicals

5. COMPETENCIE
S
Perform
operation
s on
radical
expressio
ns. M9AL-
a. differentiate like radicals
from unlike radicals
b. perform addition and
subtraction of radical
expressions
c. think and solve on real-
life word problems
involving radicals
OBJECTIVES:

6. Simplify the following radical expressions.
1. 𝟑𝟔
2. 𝟕𝟓
3.
𝟑
𝟐𝟕𝒙𝟖
4. 𝟐𝟎𝟎𝒂𝟔
RECALL
𝟔
𝟓 𝟑
𝟑𝒙𝟐 𝟑
𝒙𝟐
𝟏𝟎𝒂𝟑
𝟐

7. “4 PICS 1 WORD”

9. “ARRANGE & LEARN”
a. 4 𝟐 , 4 𝟑
b. 8 𝟑
𝒙𝒚 , 𝟑
𝒙𝒚
c. 4 𝒙 , 𝒙
d. 𝟑 𝒙 , −𝟓 𝒙
e. 𝟖 ,
𝟑
𝟖
f. 𝟒 𝟖 , −𝟐 𝟒

10. LIKE Radicals UNLIKE Radicals
a. 4 𝟐 , 4 𝟑
b. 8 𝟑
𝒙𝒚 , 𝟑
𝒙𝒚
c. 4 𝒙 , 𝒙
d. 𝟑 𝒙 , −𝟓 𝒙
e. 𝟖 ,
𝟑
𝟖
f. 𝟒 𝟖 , −𝟐 𝟒

11. Like Radicals - radicals that have
the same index and radicand.
8 𝟑
𝒙𝒚 , 𝟑
𝒙𝒚 4 𝒙 , 𝒙
Unlike Radicals - radicals with
different index and radicand.
4 𝟐 , 4 𝟑 𝟖 ,
𝟑
𝟖

12. “GUESS and CHECK”
a. 𝟓 + 𝟓 = 𝟐 𝟓
b. 𝟓 + 𝟓 = 𝟐 𝟏𝟎
c. 𝟏𝟔 + 𝟐𝟓 = 𝟗
d. 𝟒 𝟑 − 𝟐 𝟑 = 𝟐 𝟑
e. 𝟖 − 𝟖 = 𝟎

13. “GUESS and CHECK”
f.
𝟑
𝟑 + 𝟐
𝟑
𝟑 = 𝟑
𝟑
𝟑
g.
3
2 + 2
3
3 = 3
3
5
h. 4
3
2 − 2
3
3 = 2
3
5
i. 4 8 − 2 6 = 2 2
j.
3
16 + 2
3
2 = 2
3
2

14. 1. Find the value of each statement.
2. Which of the following
statements are true? Which
are false?

15. TRUE FALSE
a. 𝟓 + 𝟓 = 𝟐 𝟓 b. 𝟓 + 𝟓 = 𝟐 𝟏𝟎
c. 𝟏𝟔 + 𝟐𝟓 = 𝟗
d. 𝟒 𝟑 − 𝟐 𝟑 = 𝟐 𝟑
e. 𝟖 − 𝟖 = 𝟎
f.
𝟑
𝟑 + 𝟐
𝟑
𝟑 = 𝟑
𝟑
𝟑
g.
3
2 + 2
3
3 = 3
3
5
i. 4 8 − 2 6 = 2 2
j.
3
16 + 2
3
2 = 2
3
2
h. 4
3
2 − 2
3
3 = 2
3
5

16. Can you add/subtract the two radical
expressions with like radicals? Unlike
radicals?
How to add/subtract radical
expressions?

17. 3. Combine like radicals by combining
the coefficients of the radical term.
Addition and Subtraction of Radical Expression
1. Simplify all radicals.
2. Combine only the like radical terms:
(same radicands and same indices)
4. Perform the operation (either addition
or subtraction)

18. 𝒂𝒏
𝒙 + 𝒃𝒏
𝒙 = 𝒂 + 𝒃 𝒏
𝒙
𝑎 + 𝑏 cannot be combined.
Note:
Ex. 4 + 9 = 13
2 + 3 = 13
5 ≠ 13

19. Illustrative Examples:
𝟏. 𝟐 + 𝟐 = 𝟏 + 𝟏 𝟐 = 𝟐 𝟐
2. 𝟔 𝟖 − 𝟐 𝟖
= 𝟔 − 𝟐 𝟖
= 𝟒 𝟖 = 𝟒 𝟒 . 𝟐
= 𝟒 𝟐 𝟐 = 𝟖 𝟐
3. 𝟑
𝒙 − 𝟓𝟑
𝒙 + 𝟗𝟑
𝒙
= 𝟏 − 𝟓 + 𝟗 𝟑
𝒙
= 𝟓𝟑
𝒙

20. Illustrative Examples:
4. 𝟑 𝟓𝟎 + 𝟒 𝟓𝟎
= 𝟑 . 𝟓 𝟐 + 𝟒 . 𝟓 𝟐 = 𝟑𝟓 𝟐
= 𝟑 𝟐𝟓 . 𝟐 + 𝟒 𝟐𝟓 . 𝟐
= 𝟑𝟓 𝟐

21. 5.
The terms are unlike
radicals. Do not combine.

22. THINK-PAIR-SHARE Activity
Find the sum or difference of the following.
1. 8 𝟑 - 4 𝟑
2. 2 𝒙 - 𝒙 + 3 𝒙
3. 6 𝟑 + 7 𝟑 - 2 𝟑
4. 6 𝟐 - 5 𝟖 + 2 𝟑𝟐

23. GROUP Activity: (Practical Applications)
(Leg Traction)
To help align Deon’s
broken bone, a doctor uses
traction as shown in the
figure. Traction is applied by
fixing a weight, two pulleys
and some stainless steel
cable to a broken leg. Based
on the setup shown, how
many meters cable are used?

24. GROUP Activity: (Practical Applications)
(Garden Perimeter)
Find the perimeter of a rectangular garden whose length is
8 𝑏 feet and whose width is 3 𝑏 feet? Give your answer as a
radical expression in simplest form.

25. Criteria
Great!
(5 points)
Good!
(4 points)
U-Uh!
(3 point)
Accuracy
of the
solutions
All dimensions of
the given figures
The dimensions of
the two pools are
accurate.
The dimensions of
the pools are not
accurate.
Clarity and
Accuracy
of
Explanatio
n
Explanations of
how the length /
perimeter are
obtained are clear
and accurate
Some parts of
explanations are
unclear and
inaccurate
Generally, the
explanation is
unclear and
inaccurate.
Rubrics:

26. Generalizations
How do we add /subtract radical
expressions?
What are the important factors that you
think will help you in combining radicals?
We combine radicals through….
● factoring ● simplifying
● follow the rules on adding and subtracting radicals

27. Individual Formative Test
Perform the following:
1. -3 𝒙 +2 𝒙
2. 𝟓 𝟕 -2 𝟒𝟖
3. - 4 𝟒𝟒 + 5 𝟑

28. Remediation / Supplementary
Activities
1. 2 𝟑 + 4 𝟑
2. 6 𝟑 + 2 𝟑 - 3 𝟑
3. 2 𝟕 - 5 𝟕 - 8 𝟕
4. x 𝟐 – 3x 𝟐 + 5x 𝒙
5. 5 𝟑𝒂 + 5 𝟑𝒂 - 9 𝟑𝒂
6. 3 𝟐𝟎 - 2 𝟐𝟒 + 𝟏𝟖𝟎 - 𝟓𝟒
7. 𝟏𝟖 + 𝟐𝟎 - 𝟐𝟎𝟎 + 3 𝟖𝟎
8. 5 𝟕 - 𝟐𝟖 + 𝟔𝟑
Perform the following operation.