## Are You a Radical or Just a Square Root?

### Johnny WolfeSanta Rosa District Schools

#### Description

The inverse of squaring is finding a “square root.” Square roots are found in many formulas used in many disciplines.

#### Objectives

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

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 (if examples are to be worked on overhead) for ARE YOU A RADICAL OR JUST A SQUARE ROOT? (see attached file)
-ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES (see attached file)
-ARE YOU A RADICAL OR JUST A SQUARE ROOT? WORKSHEET (see attached file)
-ARE YOU A RADICAL OR JUST A SQUARE ROOT? CHECKLIST (see attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES. (See attached file.)

2. Have marking pens (for overhead).

3. Have ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES prepared and ready to demonstrate to students. (See attached file.)

4. Have enough copies of ARE YOU A RADICAL OR JUST A SQUARE ROOT? WORKSHEET for each student. (See attached file.)

5. Have enough copies of ARE YOU A RADICAL OR JUST A SQUARE ROOT? 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, and factoring. NOTE: This lesson does not deal with irrational numbers and complex numbers, nor does it deal with percents, scientific notation, absolute value, or logarithms.

1. Go over definition of “squaring.” Make sure students realize that –x
2 means –(x
2), not (-x)
2. Thus, parentheses are necessary for indicating the “square” of a “negative” number. (See #1 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

2. Have students complete “Warm-up activity.” (See #2 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

3. Discuss “Squares” and their inverse, “Square roots.” (See #3 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

4. Introduce students to the definition of a “Square Root.” (See #4 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

5. Present students with “Thought Provoker.” (See #5 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

6. Go over terminology with students. (See #6 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

7. Discuss “Square roots” and “negative” numbers. (See #7 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

8. Discuss various prefixes to “square roots” such as +, -, and + or - symbols. (See #8 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

9. Work example #9. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

10. Work example #10. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

11. Work example #11. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

12. Work example #12. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

13. Work example #13. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

14. Work example #14. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

15. Work example #15. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

16. Work example #16. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

17. Discuss “simplifying” a “radical” expression. (See #17 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES).

18. Introduce “Product Property of Square Roots.” (See #18 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

19. Discuss “prime factorizations” and “square roots.” (See #19 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

20. Work example #20. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

21. Discus the “Quotient Property of Square Roots.” (See #21 on attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? WORKSHEET.)

22. Work example #22. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

23. Work example #23. (See attached file: ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES.)

24. Distribute the ARE YOU A RADICAL OR JUST A SQUARE ROOT? WORKSHEET. (See attached file.)

25. Distribute the ARE YOU A RADICAL OR JUST A SQUARE ROOT? CHECKLIST. (See attached file.)

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

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

#### Assessments

The student worksheet will be collected and scored according to the ARE YOU A RADICAL OR JUST A SQUARE ROOT? CHECKLIST. (See attached file.)

#### Extensions

Students may be interested in the origin of mathematical symbols, such as “square root.” Have students research the origin of these terms.