Warm–up #5 1. Simplify 3 108 (𝑥+𝑦) 7 2. Multiply 7 + 3 2 21 −1

Warm–up #5 Solutions 1. Simplify 3 108 (𝑥+𝑦) 7 3 2∙2∙3∙3∙3 3 (𝑥+𝑦)(𝑥+𝑦)(𝑥+𝑦)(𝑥+𝑦)(𝑥+𝑦)(𝑥+𝑦)(𝑥+𝑦) =3 (𝑥+𝑦) 2 3 4(𝑥+𝑦)

Warm–up #5 Solutions 2. Multiply 7 + 3 2 21 −1 = 7 2 21 −1 7 + 3 2 21 −1 3 =2 7∙7∙3 − 7 +2 3∙3∙7 − 3 =2 7 3 − 7 +2 3 7 − 3 =14 3 − 7 +6 7 − 3 =13 3 +5 7

Homework Log Wed 9/23 Lesson 1 – 8 Learning Objective: To simplify radical expressions into simplest radical form Hw: #113 Pg. 77 #47 – 99 odd

9/23/15 Lesson 1 – 8 Simplest Radical Form Day 2 Advanced Math/Trig

Learning Objective To simplify radical expressions into simplest form

Simplest Radical Form 1. No negative or zero exponents 2. Radicand doesn’t have power ≥ index 3. No in denom 4. No fractions in 5. Index as small as possible index radicand

Rationalizing Denominator No radicals in the denominators! 1. 3 7 = 3 7 7∙7 = 3 7 7 2. 3 3 4 = 3 3 3 2∙2 = 3 3∙2 3 2∙2∙2 = 3 6 2 = 3 3 3 4 Need a group of 3 ∙ 7 7 ∙ 3 2 3 2

Rationalizing Denominator ∙ (3+ 5 ) (3+ 5 ) 3. 3 2𝑥 9 𝑦 2 = 3 2𝑥 3∙3∙𝑦∙𝑦 = 3 6𝑥𝑦 3𝑦 4. 3 3− 5 Use difference of squares (a + b)(a – b) = 𝑎 2 − 𝑏 2 = 3(3+ 5 ) (3) 2 − ( 5 ) 2 = 9+3 5 9−5 = 9+3 5 4 ∙ 3 3𝑦 3 3𝑦

Simplify 5. 6 𝑥 2 9 𝑦 10 Need groups of 6 = 6 𝑥 2 6 3 2 𝑦 10 = 6 81𝑥 2 𝑦 2 6 3 6 𝑦 12 = 6 81 𝑥 2 𝑦 2 3 𝑦 2 6. 12 𝑦 3 𝑧 24 𝑦 4 𝑧 3 Same index, reduce first! = 1 2𝑦 𝑧 2 = 2𝑦 2𝑦𝑧 ∙ 6 3 4 𝑦 2 6 3 4 𝑦 2 ∙ 2𝑦 2𝑦 = 3 9𝑥𝑦 3 𝑦 2

Simplify 7. 3 2−3 2 ∙ 2 −1 2 = 3 2 2 2 +6 3 2 −3 2 2 −3(6) (2 2 ) 2 − (6) 2 = 6 2 +18 2 −6 2 −18 4 2 −36 = −6+12 2 −28 = 3 2 −3 2 2 −3(2) ∙ 2 2 +6 2 2 +6 = 12+12 2 −18 8−36 = 3−6 2 14 Can all be divided by −2

Simplify 8. 2 27 = 2 27 = 6 3(3) = 6 9 9. 3 1 9 = 1 3 3∙3 = 3 3 3 ∙ 3 3 3 3 = 2 3 3 ∙ 3 3

Simplify ∙ 2 5 + 3 2 5 + 3 10. 2 2 5 − 3 = 2 2 5 +2 3 (2 5 ) 2 − ( 3 ) 2 = 4 5 +2 3 4 5 −3 = 4 5 +2 3 17

Simplify 11. 3 𝑥 3 + 𝑥 2 + 12𝑥+4 = 𝑥 2 (3𝑥+1) + 4(3𝑥+1) = x 3𝑥+1 +2 3𝑥+1 =(x+2) 3𝑥+1

Simplify 12. (2− 3 ) −2 = 1 (2− 3 ) 2 = 7+4 3 (7) 2 − (4 3 ) 2 = 7+4 3 1 = 7+4 3 = 1 4−4 3 +3 ∙ 7+4 3 7+4 3 = 1 7−4 3 = 7+4 3 49−16(3)

Ticket Out the Door Simplify 𝑥 3 𝑥 6 Explain what you did to simplify.

Homework #113 Pg. 77 #47 – 99 odd