1. Warm–up #4
1. Evaluate − Write as exponents 4 8𝑥 𝑦 3 3. Simplify [( 𝑥 1 3 𝑦 − 2 3 ) − 1 2 ] 6

2. Warm–up #4 Solutions
1. Evaluate − = 3 − = − = 4 25

3. Warm–up #4 Solutions
2. Write as exponents 4 8𝑥 𝑦 3 8𝑥 𝑦 Simplify [( 𝑥 1 3 𝑦 − 2 3 ) − 1 2 ] 6 = [ 𝑥 − 1 6 𝑦 1 3 ] 6 =𝑥 −1 𝑦 2 = 𝑦 2 𝑥

4. Homework Log Tues 9/22 Lesson 1 – 8 Learning Objective:
To perform operations on radical expressions
Hw: #112 Pg. 77 #1 – 45 odd

5. 9/22/15 Lesson 1 – 8 Operations with Radicals Day 1
Advanced Math/Trig

6. Learning Objective To add & subtract radicals
To multiply & divide radicals
To reduce the index

7. Operations with Radicals
𝑛 𝑎𝑏 = 𝑛 𝑎 ∙ 𝑛 𝑏 𝑛 𝑎 𝑛 =𝑎 𝑛 𝑎 𝑛 𝑏 = 𝑛 𝑎 𝑏
Assume all variables are positive 𝑥 2 = 3∙3∙3∙3∙3∙𝑥∙𝑥 Pull out groups of 2 = 3 ∙ 3 ∙ x 3 = 9x 3

8. Operations with Radicals
Assume all variables are positive 𝑥 4 𝑦 5 = 3 2∙2∙2∙2∙2∙𝑥∙𝑥∙𝑥∙𝑥∙𝑦∙𝑦∙𝑦∙𝑦∙𝑦 Pull out groups of 3 = 2 ∙ x ∙ y 3 2∙2∙𝑥∙𝑦∙𝑦 =2xy 3 4𝑥 𝑦 2

9. Adding or Subtracting Radicals
Step 1: Simplify all radicals Step 2: If same index & radicand, combine like terms 𝑛 𝑎
Radicand
Index

10. Adding or Subtracting Radicals
= =7 2 𝑥 + 𝑦 ≠ 𝑥+𝑦 = 50 =5 2 Not the same answer!
− 7 Different radicands cannot be simplified! Different index cannot be simplified!

11. Multiplying or Dividing Radicals
∙5 7 =3∙5 2∙7 =15 14
= = 3 4

12. Operations with Radicals
𝑥 2 𝑦 2 ∙ 3 12 𝑥 2 𝑦 = 3 3∙3∙3∙2∙2∙𝑥∙𝑥∙𝑥∙𝑥∙𝑦∙𝑦∙𝑦 = 3 ∙ x ∙ y 3 2∙2∙𝑥 =3xy 3 4𝑥

13. Multiplying 8. ( 5 −3 3 )( 15 −4) 75 −3 45 −4 5 +12 3 5 −3 3 15 75
8. ( 5 −3 3 )( 15 −4)
75 −3 45 −
5 3 −3(3 5 )−
5 3 −9 5 −
17 3 −13 5 5
−3 3 15 75
−3 45 −4
−4 5
12 3

14. Multiplying
9. (3−2 7 )(2+ 7 ) =6+3 7 −4 7 −2 49 =6− 7 −2 7 =6− 7 −14 =−8− 7

15. Operations on Radicals
= =5 5
11. 3a −4𝑏 3 2
=3a (2 3 2) −4𝑏 3 2
=6a 3 2 −4𝑏 3 2
=(6a−4b) 3 2

16. Reducing Radical Index
= Write in exponent form =2 3 9 =2 1 3 Convert back to radical form = 3 2

17. Reducing Radical Index
= = = = 10
𝑥 4 𝑦 8
= 𝑥 4 𝑦 8
= 𝑥 𝑦 8 12
= 𝑥 𝑦 2 3
= 3 2𝑥 𝑦 2

18. Ticket Out the Door Multiply by distributing, foiling, or box method
( 6 −3 2 )( )
Did you notice it’s a special product? What is it?
Multiply it using special product rules. Do you get the same answer?

19. Homework
#112 Pg. 77 #1 – 45 odd