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Republic of the Philippines

Department of Education

Regional Office IX, Zamboanga Peninsula

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Z est for P rogress

Z eal of P artnership

Quarter 2 – Module 7:

Operations of Radical Expressions

Name of Learner: ___________________________

Grade & Section: ___________________________

Name of School: ___________________________

Math Module – Grade 9

Alternative Delivery Mode

Quarter 2 – Module 7: Operations of Radical Expressions

First Edition, 2020

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Secretary: Leonor Magtolis Briones

Undersecretary: Diosdado M. San Antonio

Printed in the Philippines

Department of Education: Region IX, Schools Division of Zamboanga del Norte

For inquiries or feedback, please write or call: Department of Education Schools Division of Zamboanga del Norte

Capitol Drive, Estaka, Dipolog City

Fax: (065) 908 0087 | Tel: (065) 212 5843, (065) 212 5131

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Development Team of the Module Writer: : Armil O. Turtor

Reviewer: ISMAEL K. YUSOPH Management Team: SDS: Ma. Liza R. Tabilon, Ed.D, CESO V

ASDS: Dr. Ma. Judelyn J. Ramos

ASDS: Dr. Armando P. Gumapon ASDS: Dr. Judith V. Romaguera

CID CHIEF: Lilia E. Abello, Ed.D EPS-LRMS: Evelyn C. Labad

EPS-MATH: Ismael K. Yusoph PSDS: Antonina D. Gallo, Ed.D.

Principal: Daisy Flor J. Romaguera

What I Need to Know

This module is a one-lesson module. It covers key concepts of the

different operations of radical expressions. You will be skilled at simplifying

radicals through the fundamental operations. (M9AL-IIh-1)

In this lesson we will address the following questions and look at some

important real-life applications of radicals.

• How can you simplify radical expressions?

• How do you operate with radicals?

• How can the knowledge of radicals help us solve problems in daily life?

At the end of this module, you are expected to:

• perform operations on radical expressions (M9AL-IIh-1).

Perform the indicated operation.

1. 2x + 3x -5x

2. 7y + 5y2 – 3y

3. 6a (2a2bc3)

4. (x +y)(x – y)

5. 10x2yz

2x

Questions:

1. How did you know thar the given expressions are simplified?

2. What concepts have you applied?

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Lesson 1

OPERATIONS WITH RADICAL

EXPRESSIONS

What’s In

What’s New Carefully analyze the given examples.

1. Add or subtract as indicated.

Questions:

1. How did you know that the given expressions are simplified?

2. What processes have you observed?

What is It

OPERATIONS WITH RADICAL EXPRESSIONS

Radicals are either rational or irrational numbers. Like rational

numbers, irrational numbers can be added, subtracted, multiplied and

divided.

A. ADDITION AND SUBTRACTION OF RADICALS

Similar or like radicals are expressions with the same index and

radicands.

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Examples:

Only similar radicals or like radicals can be combined by addition or

subtraction .We can combine similar radicals by adding or subtracting their

coefficients and affixing their common radical.

Illustrative Examples:

1. Find the sum.

5√10 + 8√10

Check first if the two expressions can be combined or they have the same

radicand, if both have √10 as a radicand, so that means you can combine the two

expressions. You can make use of the distributive property to better understand the

addition process.

5

2

6

7

8

=

6 5400

√

To divide radicals of different orders, it is necessary to first change the

radicals to the same order and rationalize the

denominator.

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2 . Divide and simplify the result: √6 ÷ √5

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Activity 1.

Match Column A with the sum/difference of the radical problems in Column

B. Write the letter of the correct answer.

Questions:

1. How do you add radicals?

2. How do you subtract radicals?

3. Did you encounter any difficulties while solving? If yes, what will you do

to overcome those difficulties?

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What’s More

Activity 2.

Perform the indicated operations. Then, fill up the next table with the letter

that corresponds to the correct answer. When, you are done, you will be able

to decode the answer of the question.” What shall we do during pandemic?”

What I Can Do

A. Read carefully the given problem then answer the questions that follow.

1. If each side of a garden is increased by 4m, its area becomes 144 m2.

a. What is the measure of its side after increasing it?

b. What is the length of the side of the original square garden?

c. Supposing the area of a square is 192 m2, find the length of its side.

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2. A farmer is tilling a square field with an area of 900 m2. After 3 hours, he tilled 2

of the given area. 3

a. Find the the side of the square field.

b. What are dimensions of the tilled portion?

c. If the area of the square field measures 180 m2, find the length of

its side.

B. Answer the following problems completely.

Give 3 examples of situations in real life that involve operations of

radicals. In each situation,

1. formulate a problem.

2. solve the problem, and

3. explain how this particular problem may help you in formulating

conclusions and/ or making decisions.

Assessment

Choose the letter that you think best answers the question.

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3. Which of the following is the simplified form of (2 + √5 )( 5 - √3)?

A. 10 - 2√3 + 5√5 - √15 B. 10 + 3√5 - √15

C. D.10 + 5 -

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Answer Key

Message: WEAR MASK

What I Can Do

1. a. The side of the square garden is 12m after increasing it.

b. The length of the sides of the original garden is 8m.

c. Supposing the area of a square garden is 192 m2, the length of its

side is 8√3 m .

2. a. The side of the square is 30m.

b. The dimensions of the tilled portion are 30m x 20m.

c. If the area of square field measures 180 m2, the length of its side

is

Assessment

1.A 6.A

2.D 7.C

3.A 8.B

4.B 9.C

5.C 10.D

References

Dilao, Soledad Jose and Bernabe, Julieta G.,Intermediate

Algebra Mathematics 9 Learner’s Module

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What’s In

Activity 2

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