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Section 7.2

Section 7.2. Multiplying and Dividing Radicals. 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.

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Section 7.2

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  1. Section 7.2 Multiplying and Dividing Radicals

  2. 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 Multiply. Simplify if possible. b. –16 • 4 3 3 Quick Check 7-2

  3. 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 Simplify each expression. Assume all variables are positive. Quick Check 7-2

  4. 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 Multiply and simplify . Assume all variables are positive. 25xy8 • 5x4y3 Quick Check 7-2

  5. 192x8 3 3 = = 3x 3 192x8 3x 3 = 64x7 3 = 43(x2)3 • x = 4x2x 3 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Divide and simplify. Assume all variables are positive. a. b. Quick Check 7-2

  6. 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 Rationalize the denominator of each expression. Assume that all variables are positive. a. 7-2

  7. 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 (continued) a. 7-2

  8. b. x5 x5 x5 3x2y 3x2y 3x2y 3x2y 3x2y • 3x7y x3 3xy x3xy = 3x2y 3x2y 3y • = = = Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 (continued) Quick Check 7-2

  9. 10d 7 t2 = t = d 4.9 d 4.9 = d • 10 49 = 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 = 4.9t2. Express t in terms of d and rationalize the denominator. d = 4.9t2 Quick Check 7-2

  10. 3 3 –3xy3 9y 2x2 2x 3 3 2xy 5xy2 3 3 3 6x2yxy 8xy y 128x3 2xy 21x 3 7x 3 Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7-2 Assume that all variables are positive. 1. Multiply. Simplify if possible. a. 5 • 45 b. 4 • 2000 2. Simplify. a. 8x5b. –243x3y10 3. Multiply and simplify. a. 18x3 • 2x2y3b. 10x2y4 • 4x2y 4. Divide and simplify. a. 5. Rationalize the denominator of the expression. 15 20 7-2

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