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# Multiplying Radical Expressions

Lesson 9 of 11

## Objective: SWBAT multiply radical expressions and simplify their answers completely

#### Warm Up

*10 min*

I plan for this Warm Up to take the students about 15 minutes to complete and for me to review. This is longer than one of my typical Warm Ups, but I want to provide the students with several concepts and methods to multiplying radicals before they complete the Independent Practice. I compare multiplying polynomials to multiplying radicals to refresh the students memory about the distributive property and how to multiply binomials.

In the Warm Up, I provide students with several different types of problems, including:

- multiplying two radical expressions
- multiplying using distributive property with radicals
- multiplying two binomials with radicals

I model reviewing the Warm Up in the video below.

#### Resources

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#### Independent Practice

*25 min*

After reviewing the Warm Up, I work a few more examples for students before handing them the Independent Practice. I want to make sure the students understand the structure of the problem, and the different ways to multiply. I show some of those examples below in the video.

After I work the examples, students begin to work on the Independent Practice. I walk around to monitor student progress and to assist students when needed. Several students struggled with multiplying the binomials. It seemed to help students when I take the first term, set it outside of the second parentheses to show distributive to multiply it to both terms. Then, repeat the same procedure for the second term in the first parentheses.

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#### Exit slip

*15 min*

I hand the Exit slip to students about the last 15 minutes of class. Again, like the Warm Up, I am allowing more time in this lesson for students to complete the Exit Slip. In this Exit Slip, I instruct the students to find the area of the irregular shape. Students have to sketch lines on the diagram to find regular shapes that they can use a formula to find the area. Then they can find the sum of all the parts or areas.

I use this Exit Slip as a quick formative assessment to check for student understanding of multiplying radical expressions.

The reason I allow more time is that the third goal is for students to critique each others work in a nice manner. The stronger students get at this skill, the better the class community. Math Practice 3 helps students learn from correct answers, wrong answers, and conversations.

#### Resources

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*Responding to Rhonda Leichliter*

Yes, that was a messy bit of work to do the trapezoid's height, I have enjoyed your work:) Thanks for the revision.

| 2 years ago | Reply*Responding to stacey rose*

I will post a key to the problem. It is not how I originally planned this problem. Instead of just dividing 12 square root of 3 in half to get the base of one of the triangles, square root of 7 must be subtracted from 12 square root of 3 then divided by 2. This gives you a binomial with radicals to square for the Pythagorean Theorem. I think it would be easier to form a Pentagon with a triangle on top instead of a trapezoid. I will submit a second Exit slip in my reflection with the revision. Thank You for your feedback.

Rhonda Leichliter

| 2 years ago | Reply

can you tell me how you split up the irregular shape on the exit slip? I am not finding a good solution. thanks

| 2 years ago | Reply

*expand comments*

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Radicals
- LESSON 2: Apply the Pythagorean Theorem to a Broken Telephone Pole and an Isosceles Right Triangle.
- LESSON 3: The Pythagorean Theorem and the Distance Formula
- LESSON 4: Finding the Distance or the Midpoint of a Line Segment on the Coordinate Plane
- LESSON 5: Tailgating and Solving Radical Equations
- LESSON 6: Renovate a Park by Applying Radicals and Formulas
- LESSON 7: Add and Subtract Radical Expressions
- LESSON 8: Gallery Walk of Application Problems Involving Radicals
- LESSON 9: Multiplying Radical Expressions
- LESSON 10: Dividing Radicals Made Easy Through the History of Rationalizing
- LESSON 11: Simplify and Rewrite Radicals as Rational Exponents and Vice Versa.