1. Algebra 2 Lesson 7-2 (Page 368) ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

2. To Multiply Radical Expressions ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

3. If and are real numbers, Then. ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

4. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Multiply. Simplify if possible. b.–16 4 a.3 12 3 12 =3 12 =36 = 6 The property for multiplying radicals does not apply. –4 is not a real number. c.–4 16 3 3 7-2 33 3 3 –16 4 =–16 4 =64 = –4

5. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Multiply. Simplify if possible. 7-2 a. 6 b. c. 36 d. a. –3 b. 3 c. not possible d. 27 a. 4 b. –4 c. not possible d. 2

6. a.50x 5 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Simplify each expression. Assume all variables are positive. = 5x 2 2xdefinition of nth root Factor into perfect squares. 50x 5 =5 2 2 (x 2 ) 2 x 3 b.54n 8 3 3 54n 8 =3 3 2 (n 2 ) 3 n 2 Factor into perfect cubes. 3 = 3n 2 2n 2 definition of nth root 7-2 3 3 =33(n2)3 2n2=33(n2)3 2n2 nnn a b = ab =5 2 (x 2 ) 2 2 x nnn a b = ab

7. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Simplify each expression. Assume all variables are positive. 7-2 a. b. c. d.

8. 33 25xy 8 5x 4 y 3 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Multiply and simplify. Assume all variables are positive. 3 = 5 3 x 3 (y 3 ) 3 x 2 y 2 Factor into perfect cubes. 3 = 5xy 3 x 2 y 2 definition of nth root 7-2 33 =53x3(y3)3 x2y2=53x3(y3)3 x2y2 nnn a b = ab 25xy 8 5x 4 y 3 = 25xy 8 5x 4 y 3 333 nnn a b = ab

9. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Multiply and simplify Assume all variables are positive. 7-2 a. b. c. 66x 3 y d. 42xy

10. To Divide Radical Expressions ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

11. If and are real numbers, and, then. ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

12. 3 =64x 7 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Divide and simplify. Assume all variables are positive. a. 3 =–27 3 =(–3) 3 = –3 3 –81 3 3 = b. 3x3x 3 3 192x 8 = 3x 3 = = 4x 2 x 3 3 =4 3 (x 2 ) 3 x 7-2 = 3 –81 3

13. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Divide and simplify. Assume all variables are positive. 7-2

14. To of an expression, rewrite it so there are no Radicals in any denominators. ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

15. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Rationalize the denominator of each expression. Assume that all variables are positive. 15 5 = a. 5 3 7-2 Method 1: Rewrite as a square root of a fraction. 3535 = 5 3 = 3 5 5 Then make the denominator a perfect square. = 15 5 2

16. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 (continued) 3 5 5 Multiply the numerator and denominator by 5 so the denominator becomes a whole number. = 3 5 Method 2: a. 15 5 = 7-2 5 3

17. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 (continued) b. x5x5 3x2y3x2y c. 3 54y54y x5x5 3x2y3x2y x5x5 3x2y3x2y 3x2y3x2y3x2y3x2y = 3x7y3x7y 3x2y3x2y = x 3 3xy 3x2y3x2y = x 3xy 3y3y = 3 5 4 2 y 2 4y 4 2 y 2 3 54y54y = Rewrite the fraction so the denominator is a perfect cube. 3 80y 2 4 3 y 3 = 2 10y 2 4y 3 = 10y 2 2y 3 = 7-2

18. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 7-2

19. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 The distance d in meters that an object will fall in t seconds is given by d = 4.9t 2. Express t in terms of d and rationalize the denominator. d = 4.9t 2 t 2 = d 4.9 t = d 4.9 10d 7 = d 10 49 = 7-2

20. Algebra 2 Lesson 7-2 (Page 368) ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2