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

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

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

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

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

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 n 8 =3 3 2 (n 2 ) 3 n 2 Factor into perfect cubes. 3 = 3n 2 2n 2 definition of nth root =33(n2)3 2n2=33(n2)3 2n2 nnn a b = ab =5 2 (x 2 ) 2 2 x nnn a b = ab

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

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 =53x3(y3)3 x2y2=53x3(y3)3 x2y2 nnn a b = ab 25xy 8 5x 4 y 3 = 25xy 8 5x 4 y nnn a b = ab

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

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

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

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 – = b. 3x3x x 8 = 3x 3 = = 4x 2 x 3 3 =4 3 (x 2 ) 3 x 7-2 = 3 –81 3

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

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

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

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

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 = y 2 4y 4 2 y y54y = Rewrite the fraction so the denominator is a perfect cube. 3 80y y 3 = 2 10y 2 4y 3 = 10y 2 2y 3 = 7-2

Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON

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 d 7 = d = 7-2

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