1. 11.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Simplify Radical Expressions

2. 11.2 Warm-Up Use the distributive property to write an equivalent expression. 1.2(x + 6) 2.x(x 2 + 2) ANSWER 2x + 12 ANSWER x 3 + 2x 3.(x + x 2 )(–3) 4.0.1(6 + 10x) ANSWER –3x – 3x 2 ANSWER 0.6 + x

3. 11.2 Warm-Up ANSWER about 12.2 m 5. The area of a square field is 148 square meters. What is the side length of the field?

4. 11.2 Example 1 a. Factor using perfect square factor. Product property of radicals Simplify. Factor using perfect square factors. Product property of radicals 32 = 16 2 = 162 = 4 2 b. x3x3 9 = 9x2x2 x = 9x2x2 x = 3x3xx Simplify.

5. 11.2 Guided Practice (a) Simplify and. 1. 24 (b)x2x2 25 (a) 2 6 and (b) 5x ANSWER

6. 11.2 Example 2 a. Product property of radicals Simplify. Product property of radicals = 6 = 36 6 = 6 6 Simplify. Multiply. = x2x2 34 = x2x2 43 = 3x3xx4b.3x3x4x 4x4x3 = Multiply. Product property of radicals Simplify.

7. 11.2 Example 2 c. Product property of radicals Simplify. Product property of radicals =73xy Multiply. 3x7x7xy2y2 = 7x7xy2y2 x 3= 37x7xy2y2 2 = 7x2x2 3y2y2 Simplify.

8. 11.2 Example 3 a. Simplify. 13 100 = 13 100 = 10 13 Quotient property of radicals b. 7 x2x2 = 7 x2x2 = x 7 Simplify. Quotient property of radicals Simplify.

9. 11.2 Guided Practice Simplify (a) and (b). 2. xx3x3 2 1 y2y2 (a) x2 2 and (b) y 1 ANSWER

10. 11.2 Example 4 a. Product property of radicals Simplify. 7 5 = 7 5 7 7 = 49 75 = 7 75 Multiply by. 7 7 Simplify the expression.

11. 11.2 Example 4 b. Product property of radicals Simplify. Product property of radicals 3b3b 2 = 3b3b 3b3b3b3b 2 = 9b9b 6b6b 2 = b2b2 9 6b6b = 6b6b 3b3b Multiply by. 3b3b 3b3b

12. 11.2 Guided Practice 3. 3 1 = 3 3 Simplify the expression. 4. x 1 = x x 5. 3 2x2x = 2x2x 2x2x 3

13. 11.2 Example 5 Simplify the expression. a. Simplify. 4 Product property of radicals 10 Commutative property 13 + – 910 = 4 – 91013 += (4 – 9)1013 + –510 13 += Distributive property 35b. + 4816 3 = 35 + = 3(5 + 4) = 35 + 163 = 3534 + 39 = Factor using perfect square factor. Distributive property Simplify.

14. 11.2 Guided Practice 6. 72 + 633 711 = Simplify the expression.

15. 11.2 Example 6 Simplify the expression. a. Simplify. ( 4 – 5 Product property of radicals 20 Distributive property Simplify. ) = 4–2055 = 45– 100 = – 1045 b. + –3 ( )() 2727 = 7 273 – + 2 – 3 () 2 = 14 7 – 3 + – 6 = 1 – 2 Multiply. Product property of radicals Simplify. = ( ) ( ) ( + 2+ + –3 2 7727–3 ) 22

16. 11.2 Guided Practice Simplify the expression. 7. ( ) 5 4 – ( ) 1 – 5 9 – 55 ANSWER

17. 11.2 Example 7 ASTRONOMY a. Simplify the formula. b. Jupiter’s average distance from the sun is shown in the diagram. What is Jupiter’s orbital period? The orbital period of a planet is the time that it takes the planet to travel around the sun. You can find the orbital period P (in Earth years) using the formula P = d where d is the average distance (in astronomical units, abbreviated AU) of the planet from the sun. 3

18. 11.2 Example 7 = 2 d Product property of radicals Simplify. SOLUTION = 3 a.Pd = 2 dd = d d Factor using perfect square factor. Write formula. b. Substitute 5.2 for d in the simplified formula. = 5.2 = Pd d The orbital period of Jupiter is 5.2, or about 11.9, Earth years. ANSWER 5.2

19. 11.2 Guided Practice 8. Neptune’s average distance from the sun is about 6 t imes Jupiter’s average distance from the sun. Is the orbital period of Neptune 6 times the orbital period of Jupiter? Explain. ASTRONOMY No. Neptune’s orbital period is Thus, Neptune’s orbital period is 6 6 times the orbital period of Jupiter. ANSWER

20. 11.2 Lesson Quiz 1. 56a 2 Simplify the expression. 2a 14 ANSWER 2. b 64 b 8 ANSWER 3. 5 2 – 2 8 + 6 2 + 6 ANSWER

21. 11.2 Lesson Quiz 3h3h 2 A person is standing on a cliff, with an eye level at 60 feet, looking out across the ocean. Using the formula d = where d (in miles) is the distance a person can see to the horizon and h (in feet) is the person’s eye level above the water to find the number of miles the person can see to the horizon. 4. about 9.5 mi ANSWER