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

2. Warm–up #5 Solutions
1. Simplify (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)

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

4. 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

5. 9/23/15 Lesson 1 – 8 Simplest Radical Form Day 2
Advanced Math/Trig

6. Learning Objective
To simplify radical expressions into simplest form

7. 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

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

9. Rationalizing Denominator
∙ (3+ 5 ) (3+ 5 )
𝑥 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
= −5 =
∙ 3 3𝑦 3 3𝑦

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

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

12. Simplify =
= (3) =
= 1 3 3∙3 = 3 3 3 ∙ = ∙

13. Simplify ∙
− 3 = (2 5 ) 2 − ( 3 ) 2 = −3 =

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

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

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

17. Homework
#113 Pg. 77 #47 – 99 odd