1. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

2. Make sure you know the day and time of the final exam for this section of Math 110: All Math 110 finals will be given in your regular classroom. (Next slide shows final exam schedules for all sections.)

3. Wednesday 12/16Thursday 12/17Friday 12/18Monday 12/21Tuesday 12/22 8:00 to 10:00 Scheduled Final in 214: LAB CLOSED 110-001 Neiderhauser 8:00110-002 Lee 10:10010-003 DKL MW 12:20110-005 Lee 2:30 10:00 to 12:00 Scheduled Final in 245: 010-004 Corne TTh 2:30 12:00 to 2:00 Scheduled Final in 214: 110-006 Lee 3:35010-001 DKL MW 9:05110-003 Schmidt 11:15110-004 Thielman 1:25 2:00 to 4:00 Scheduled Final in 214: LAB CLOSED 010-002 Mayer TTh 9:05 4:00 to 6:00 Scheduled Final in 214: 110-007 Hulett 4:40 6:00 to 8:00 Scheduled Final in 214: LAB CLOSED 110-008 Hulett 5:45

4. Section 10.3 Simplifying Radical Expressions

5. Examples: Recall these square root problems from Section 10.1: (7 2 ) ½ =

6. What we did in the previous examples was essentially to divide the exponent of each base by 2, which is index of the radical for square roots. Think of this as dividing the exponent 7 by the index 2 Two goes into seven 3 times with a remainder of 1

7. Example Simplify First, break down 12 into its prime factors: 12 = 4∙3 = 2∙2∙3 = 2 2 ∙3 1 This gives Now divide the exponents by 2 (square root, so the index is 2). Answer:

8. Problem from today’s homework: Start by breaking down 396: 396 (use your calculator, and start by dividing by 2) 2 198 2 99 9 11 3 3 So 396 = 2 2 3 2 11 1 2 2 3 2 11 1 x 6 y 15 Final Answer: -

9. If we have a radical with an index of 3 or higher, we can use the same process to simplify the radical. Divide the exponent 7 by the index 3 Three goes into seven 2 times with a remainder of 1

10. Example Simplify Answer:

11. Problem from today’s homework:

12. If and are real numbers, then Why is this condition important? No, because square roots of negative numbers are not real numbers. Product and Quotient Rules for Radicals: Product Rule: Quotient Rule: Because division by zero gives an undefined quotient.

13. Simplify the following radical expressions. Example (Assume x and y are ≥ 0) (Assume a > 0 and b ≠ 0)

14. Problem from today’s homework:

15. 5

16. Example Use the quotient rule to divide, then simplify if possible: Answer:

17. In previous chapters, we’ve discussed the concept of “like” terms. These are terms with the same variables raised to the same powers. They can be combined through addition and subtraction. Example: (x 2 + 5x – 1) + (6x 2 - 3x + 4) = 7x 2 + 2x + 3 Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand.

18. Like radicals are radicals with the same index and the same radicand. Like radicals can also be combined with addition or subtraction by using the distributive property.

19. Can not simplify (different indices) Can not simplify (different radicands) Example

20. Always simplify radicals FIRST to determine whether there are like radicals to be combined.

21. Simplify the following radical expression. Example

22. REMINDER: The assignment on today’s material (HW 10.3) is due at the start of the next class session. Please open your laptops and work on the homework assignment until the end of the class period. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in on the Math 110 clipboard by the front door of the lab