CH 7 2 Multiplying and Dividing Radical Expressions

CH. 7. 2 Multiplying and Dividing Radical Expressions

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

Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7 -2 Simplify each expression. Assume all variables are positive. a. 50 x 5 = = 52 • (x 2)2 • x Factor into perfect squares. 52 • (x 2)2 • n = 5 x 2 b. 3 3 2 • x 2 x a • n b = n ab definition of nth root 54 n 8 = = 3 3 33 • 2 • (n 2)3 • n 2 33(n 2)3 • = 3 n 2 3 2 n 2 Factor into perfect cubes. n a • n b = n ab definition of nth root 7 -2

Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7 -2 Multiply and simplify are positive. 3 25 xy 8 • 3 5 x 4 y 3 = = = 3 3 25 xy 8 • n 25 xy 8 • 5 x 4 y 3 = 5 xy 3 3 3 n 5 x 4 y 3. Assume all variables b = n ab Factor into perfect cubes. 53 x 3(y 3)3 • x 2 y 2 53 x 3(y 3)3 • a • 3 x 2 y 2 n a • n b = n ab definition of nth root 7 -2

Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7 -2 Divide and simplify. Assume all variables are positive. a. 3 = b. – 81 3 3 = 192 x 8 3 3 – 81 3 = = 3 – 27 = = 3 (– 3)3 = 3 3 192 x 8 3 x 64 x 7 43(x 2)3 • x = 4 x 2 = – 3 7 -2 3 x 3 x

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

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

Multiplying and Dividing Radical Expressions ALGEBRA 2 LESSON 7 -2 (continued) b. c. x 5 3 5 4 y 3 x 2 y x 5 3 x 2 y = = x 5 • 3 x 2 y 3 x 7 y 3 x 2 y = x 3 3 xy 2 3 x y = x 3 xy 3 y = = 7 -2 3 5 • 4 2 y 2 4 y • 42 y 2 3 80 y 2 43 y 3 2 3 3 10 y 2 4 y 10 y 2 2 y Rewrite the fraction so the denominator is a perfect cube.

Homework Page 371, Exercises: 2 – 54 (EOE)