This document provides information and examples on multiplying radical expressions. It discusses the properties for multiplying radicals of the same order and binomials involving radicals. Examples are provided to simplify radical expressions using these properties. The document also discusses how to multiply radicals with different indices by writing the radicands in fractional exponents and changing the fractions to have a common denominator before multiplying the radicals. Students are provided with practice problems to simplify expressions involving multiplication of radicals.

1. 32

2. 4
x4

3. a2b

4. 18

5. 50

6. OPERATIONS ON
RADICALS
a. Perform multiplication on radical expressions
b. Solve problems involving multiplication of radical expressions
c. Appreciate architectural skills in accurate planning

7. Find the product of the following
radical expression in the box.

8. Consider these products of radicals.
1. a ⦁ b = ab
2.3
a ⦁
3
b =
3
ab

9. Examples
A. Simplify: 𝟑 𝟐 ⦁ 𝟔
3 2 ⦁ 6 = 3 12
= 3 4 ⦁ 3
= 3 ⦁ 2 3
= 6 3

10. Examples
B. Simplify: 𝟐 𝒙 ⦁ 𝟓 𝟔𝒙⦁ 𝟐𝐱
2 𝑥 ⦁ 5 6𝑥⦁ 2𝑥 = 10 12𝑥3
= 10 4 ⦁ 3⦁ 𝑥2⦁𝑥
= 10 ⦁ 2 ⦁ 𝑥 3𝑥
= 20𝑥 3𝑥

11. Example:
Multiply the binomials and simplify:
( 2 + 3)(4 2 − 2 3)
( 2 + 3)(4 2 − 2 3) = 2 ⦁ 4 2 + 3 ⦁ 4 2 − 2 3 ⦁ 2 − 2 3 ⦁ 3
= 4 4 + 4 6 − 2 6 − 2 9
= 4 ⦁ 2 + 2 6 − 2 ⦁ 3
= 8+2 6 − 6
= 2+2 6

12. Example:
Multiply 6 by
3
5
6 = 6
1
2 or 6
3
6 =
6
63
3
5 = 5
1
3 or 5
2
6 =
6
52
Thus,
6
63 ⦁
6
52 =
6
216 ⦁
6
25 =
6
5400

13. FIND THE PRODUCT
7 𝟐 ⦁ 𝟏𝟎

14. FIND THE PRODUCT
( 𝟓 + 𝟐)(𝟐 𝟓 − 𝟑 𝟐)

15. FIND THE PRODUCT
3 by
3
5

16. ACTIVITY:
It is a word prayer that is annually held
every December 24 before the beginning
of the midnight mass, Who is it?

17. 1. 2 ∙ 2 7 =
2. 5 3 ∙ 3 2 =
3. 2 10 ∙ 3 8 =
4. 3 2𝑥 ∙ 4 6𝑥2 =
5. 2 5 (3 2 + 3) =
6.
4
2 ∙
3
2 =
2 14
15 6
12 15
24x 𝑥
6 10 + 2 15
12
128
22 − 2 2
36
30 2
Answer:

18. REMEMBER!
To multiply radicals of the same order,
• use the property
𝑛
𝑎𝑏 = 𝑎
𝑎 ∙
𝑛
𝑏 then
• simplify by removing the perfect nth powers from the radicand.
To multiply binomials involving radicals,
• use the property for the product of two binomials
( a ± b )( c ± d ) = ac (ad ± bc ) ± bd, then
• simplify by removing perfect nth powers from the radicand or
• by combining similar radicals.

19. REMEMBER!
To multiply two radicals with different indices, we follow the steps below;
a. Write each radicand in fractional exponent.
b. Change the fractional exponents to similar fractions.
c. Change each back to radical form.
(The two radicals will now have the same index.)
d. Multiply the radicals and simplify.

20. DIRECTIONS: SIMPLIFY BY MULTIPLYING RADICALS.
ASSUME THAT THE VARIABLES ARE POSITIVE.
SHOW YOUR SOLUTIONS ON THE SPACE PROVIDED.
1. 8x ⦁ 4x ⦁ 3x
2.
3
5 + 2
3. 4 2 + 2 3 3 − 3 2

21. ASSIGNMENT
Study Division of Radicals
a. Define rationalization.
b. Discuss how to perform division of radicals.
Reference: Grade 9 Learner’s Material pp.
266-267