## Doing Battle with Radical Equations

### Johnny WolfeSanta Rosa District Schools

#### Description

Equations containing radicals with variables in the radicand are called radical equations. To solve such equations, first isolate the radical on one side of the equation and then square each side of the equation to eliminate the radical.

#### Objectives

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

-Overhead transparencies (if examples are to be worked on overhead) for DOING BATTLE WITH RADICAL EQUATIONS (see attached file)
-DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES (see attached file)
-DOING BATTLE WITH RADICAL EQUATIONS WORKSHEET (see attached file)
-DOING BATTLE WITH RADICAL EQUATIONS CHECKLIST (see attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES. (See attached file.)
2. Have marking pens (for overhead).
3. Have DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES prepared and ready to demonstrate to students. (See attached file.)
4. Have enough copies of DOING BATTLE WITH RADICAL EQUATIONS WORKSHEET for each student. (See attached file.)
5. Have enough copies of DOING BATTLE WITH RADICAL EQUATIONS 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, inverse operations, radicals, factoring, and solving equations.

1. Review inverse operations. (See #1 on attached file: DOING BATTLE WITH RADICAL EQUATIONS? EXAMPLES.) Answer students' questions and comments.

2. Have students do Warm-up activity. Go through this activity with students making sure they understand the concept of inverse operations. (See #2 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

3. Discuss squaring and square roots with students. Make sure that the students understand that squaring and square roots are inverse operations. (See #3 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

4. Describe the terminology that will be used (radicand, radicals, and radical equations). Also describe how we are going to solve an equation involving radicals. (See #4 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

5. Have the students work the four examples on #5. (See attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Pay special attention to the use of squaring with inverse operations. Answer students' questions and comments.

6. Discuss the importance of “checking” solutions. (See #6 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

7. Work example #7. (See attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

8. Work example #8. (See attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

9. Work example #9. (See attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

10. Work example #10. (See attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

11. Work example #11. (See attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

12. Discuss why you must check solutions. (See #12 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

13. Discuss extraneous” values. (See #13 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

14. Discuss the importance of isolating the radical. Show an example. (See #14 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.) Answer students' questions and comments.

15. Distribute the DOING BATTLE WITH RADICAL EQUATIONS WORKSHEET. (See attached file.)

16. Distribute the DOING BATTLE WITH RADICAL EQUATIONS CHECKLIST. (See attached file.)

17. The students will write their responses on the worksheet.

18. Move from student to student observing the students' work and lending assistance.

19. Assess the activity.

#### Assessments

The student worksheet will be collected and scored according to the DOING BATTLE WITH RADICAL EQUATIONS CHECKLIST. (See attached file.)

#### Extensions

Give students real-world application problems involving radicals. Have students solve these problems and determine if the solution is reasonable. (See #15 on attached file: DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES.)