## Simplifying Square Roots

### Johnny WolfeSanta Rosa District Schools

#### Description

The square root of a positive integer is in simplest form if the radicand has no perfect square factor other than one.

#### Objectives

Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.

#### Materials

-Overhead transparencies for SIMPLIFYING SQUARE ROOTS (see attached file)
-SIMPLIFYING SQUARE ROOTS Examples (see attached file)
-SIMPLIFYING SQUARE ROOTS Worksheet (see attached file)
-SIMPLIFYING SQUARE ROOTS CHECKLIST (see attached file)

#### Preparations

1. Prepare transparencies for SIMPLIFYING SQUARE ROOTS EXAMPLES if using as an overhead transparency. (See attached file.)

2. Have marking pens (for overhead).

3. Have SIMPLIFYING SQUARE ROOTS EXAMPLES prepared and ready to demonstrate to students. (See attached file.)

4. Have enough copies of SIMPLIFYING SQUARE ROOTS WORKSHEET for each student. (See attached file.)

5. Have enough copies of SIMPLIFYING SQUARE ROOTS CHECKLIST for each student. (See attached file.)

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills, such as addition, subtraction, multiplication, division, exponents, fractions, decimals, distributive property, prime factorization, absolute value, and factoring. NOTE: This lesson does not address fractions, decimals, percents, scientific notation, and logarithms.

1. Go over the definition for a “simplified form” for a square root. (See #1 on attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.)

2. Have students analyze different forms of a square root. (See #2 on attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.) Make sure that students understand that each of the forms names the same number.

3. Go over the “Product Property of Square Roots.” (See #3 on attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.)

4. Work example #4. (See attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.) Answer students' questions and comments.

5. Work example #5. (See attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.) Answer students' questions and comments.

6. Discuss “principal square root” and “nonnegative” results. Introduce the need for “absolute values” on some terms. (See #6 on attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.)

7. Discuss the rule of “odd” and “even” exponents as it deals with “absolute value.” (See #7 on attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.)

8. Work example #8. (See attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.) Answer students' questions and comments.

9. Work example #9. (See attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.) Answer students' questions and comments.

10. Work example #10. (See attached file: SIMPLIFYING SQUARE ROOTS EXAMPLES.) Answer students' questions and comments.

11. Distribute the SIMPLIFYING SQUARE ROOTS WORKSHEET. (See attached file.)

12. Distribute the SIMPLIFYING SQUARE ROOTS CHECKLIST. (See attached file.)

13. The student will write their responses on the worksheet.

14. The teacher will move from student to student observing the students work and lending assistance.

15. The teacher will assess the activity.

#### Assessments

The student worksheet will be collected and scored according to the SIMPLIFYING SQUARE ROOTS CHECKLIST. (See attached file.)

#### Extensions

Have students find the area of rectangles whose length and width involve square roots