Algebra 2 Multiplying, Dividing, Rationalizing and Simplifying… Section 7-2

Algebra 2 Objectives To multiply radical expressions To simplify radical expressions To multiply and simplify radical expressions To find roots of quotients To divide radical expressions Solve algebraic equations involving radical expressions Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Objectives To multiply radical expressions To simplify radical expressions To multiply and simplify radical expressionsTo multiply and simplify radical expressions To find roots of quotients To divide radical expressions Solve algebraic equations involving radical expressions Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Property Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiply Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Factor and Simplify Radical Expressions Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Simplify Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Simplify Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiplying and Dividing Radical Expressions 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 Additional Examples

Algebra 2 a.50x 5 Multiplying and Dividing Radical Expressions 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 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 Additional Examples

Algebra xy 8 5x 4 y 3 Multiplying and Dividing Radical Expressions 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 33 =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 Additional Examples

Algebra 2 Property To find the k th root of a quotient, find the k th root of the numerator and denominator separately. Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Dividing Radical Expressions To divide radical expressions with the same index, divide the radicands. Simplify if possible. Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Dividing Variables w/ Exponents Reminder: When Multiplying Expressions with similar Bases the Exponents ADD! When Dividing Expressions with similar Bases the Exponents SUBTRACT! Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 3 =64x 7 Multiplying and Dividing Radical Expressions 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 = 3 –81 3 Additional Examples

Algebra 2 Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Rationalizing the Denominator Writing the result without radicals in the denominator. Multiply by a 1 to make the denominator a perfect power. Multiplying and Dividing Radical Expressions Lesson 7-2

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

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

Algebra 2 Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiplying and Dividing Radical Expressions 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 = Additional Examples

Algebra 2 Multiplying and Dividing Radical Expressions 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 = Additional Examples

Algebra 2 Multiply and Simplify Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiply and Simplify Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Multiply and Simplify Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 Do I have to Multiply and Simplify…Can’t I just Factor then Simplify? Multiplying and Dividing Radical Expressions Lesson 7-2

Algebra 2 xx2x2 x 3 x4x4 x5x

Algebra 2 Homework Page

Algebra 2 Multiply and Simplify Simplify

Algebra 2