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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.

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Multiplying and Dividing Radical Expressions

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  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

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