Warm–up #4 1. Evaluate − 8 125 2 3 2. Write as exponents 4 8𝑥 𝑦 3 3. Simplify [( 𝑥 1 3 𝑦 − 2 3 ) − 1 2 ] 6

Warm–up #4 Solutions 1. Evaluate − 8 125 2 3 = 3 − 8 125 2 = − 2 5 2 = 4 25

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

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

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

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

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. 1. 243 𝑥 2 = 3∙3∙3∙3∙3∙𝑥∙𝑥 Pull out groups of 2 = 3 ∙ 3 ∙ x 3 = 9x 3

Operations with Radicals Assume all variables are positive. 2. 3 32 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

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

Adding or Subtracting Radicals 2. 32 + 18 =4 2 +3 2 =7 2 𝑥 + 𝑦 ≠ 𝑥+𝑦 32+18 = 50 =5 2 Not the same answer! 3. 3 +5 2 − 7 Different radicands cannot be simplified! 4. 3 5 + 6 4 Different index cannot be simplified!

Multiplying or Dividing Radicals 5. 3 2 ∙5 7 =3∙5 2∙7 =15 14 6. 3 20 3 5 = 3 20 5 = 3 4

Operations with Radicals 7. 3 9 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

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

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

Operations on Radicals 10. 20 + 45 =2 5 +3 5 =5 5 11. 3a 3 16 −4𝑏 3 2 =3a (2 3 2) −4𝑏 3 2 =6a 3 2 −4𝑏 3 2 =(6a−4b) 3 2

Reducing Radical Index 12. 9 8 = 9 2 3 Write in exponent form =2 3 9 =2 1 3 Convert back to radical form = 3 2

Reducing Radical Index 13. 4 100 = 4 10 2 =10 2 4 =10 1 2 = 10 14. 12 16 𝑥 4 𝑦 8 = 12 2 4 𝑥 4 𝑦 8 =2 4 12 𝑥 4 12 𝑦 8 12 =2 1 3 𝑥 1 3 𝑦 2 3 = 3 2𝑥 𝑦 2

Ticket Out the Door Multiply by distributing, foiling, or box method ( 6 −3 2 )( 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?

Homework #112 Pg. 77 #1 – 45 odd