1 / 20

Multiplying and Dividing Radical Expressions

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

kane
Download Presentation

Multiplying and Dividing Radical Expressions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 1 To Multiply Radical Expressions 7-2

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

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

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

  6. Factor into perfect squares. a. 50x5 definition of nth root 50x5 = 52 • 2 • (x2)2 • x = 52 • (x2)2 • 2 • x 3 b. 54n8 3 54n8 = 33 • 2 • (n2)3 • n2 Factor into perfect cubes. 3 = 5x2 2x a • b = ab a • b = ab 3 n n n n n n 3 = 33(n2)3 • 2n2 3 = 3n2 2n2 definition of nth root Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Simplifying Radical Expressions Simplify each expression. Assume all variables are positive. 7-2

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

  8. 3 3 3 3 3 Factor into perfect cubes. 3 25xy8 • 5x4y3 = 25xy8 • 5x4y3 = 53x3(y3)3 • x2y2 3 3 = 53x3(y3)3 • x2y2 = 5xy3x2y2 definition of nth root 3 a • b = ab a • b = ab n n n n n n Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Multiplying Radical Expressions Multiply and simplify . Assume all variables are positive. 25xy8 • 5x4y3 7-2

  9. Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Check for Understanding Multiply and simplify Assume all variables are positive.  a.  b.  c. 66x3 y d. 42xy 7-2

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

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

  12. = 192x8 3 –81 3 3 3 3 = = 3x –81 3 3 = 3 3 3 192x8 3x 3 = 64x7 = –27 3 = 43(x2)3 • x = (–3)3 = 4x2x 3 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Dividing Radicals Divide and simplify. Assume all variables are positive. a. b. = –3 7-2

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

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

  15. 3 3 Method 1: Rewrite as a square root of a fraction. 3 5 = 5 5 Then make the denominator a perfect square. 3 • 5 5 • 5 = 15 52 = = 5 15 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Rationalizing the Denominator Rationalize the denominator of each expression. Assume that all variables are positive. a. 7-2

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

  17. c. b. x5 x5 x5 3x2y 3x2y 3x2y 3x2y 3x2y • 3x7y x3 3xy x3xy 5 4y 5 4y 3 3 5 • 42y2 4y • 42y2 = = 3 3x2y 3x2y 3y • Rewrite the fraction so the denominator is a perfect cube. = = 10y2 2y 3 2 10y2 4y 80y2 43y3 3 = 3 = = = Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Rationalizing the Denominator (continued) 7-2

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

  19. 10d 7 t2 = t = d 4.9 d 4.9 = d • 10 49 = Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 HOT The distance d in meters that an object will fall in t seconds is given by d = 4.9t2. Express t in terms of d and rationalize the denominator. d = 4.9t2 7-2

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

More Related