University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

322

Pages:

1
Author:

princesa035c6tg

Mini-Lecture 8.4 Multiplying and Dividing Radicals Learning Objectives: 1. 2. 3. 4. 5. Multiply radicals. Divide radicals. Rationalize denominators. Rationalize using conjugates. Key Vocabulary: product rule for radicals, quotient rule for radicals, rationalizing, conjugates. Examples: 1. Multiply and simplify. Assume that all variables represent positive real numbers. 2. a) 3i 5 d) (3 x ) g) ( b) 5x i 5x c) 2i 6 e) 5 x 3 i 15 x f) 6 2 7 +3 )( 7 −3 ) ( )( h) 8 5 + 9 9 5 + 3 ) i) ( (4 3+ 2 3 −8 ) ) 2 Divide and simplify. Assume that all variables represent positive real numbers. 12 3 a) 50 2 b) c) 50 y 3 2y 3. Rationalize each denominator and simplify. Assume that all variables represent positive real numbers. 7 5 a) b) 5 12 c) 3x 2 4. Rationalize each denominator and simplify. Assume that all variables represent positive real numbers. a) 2 6− 3 b) 7 5+2 c) 15 3+ x Teaching Notes: • Many students have trouble with problem 1i. They tend to square each term in the binomial rather than squaring the binomial. • Most students are able to rationalize a denominator with one term. • Many students have difficulty rationalizing a denominator with 2 terms. • Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 15 ; 1b) 5x ; 1c) 2 3 ; 1d) 9x ; 1e) 5 x 2 3 ; 1f) 3 2 + 2 3 ; 1g) -2; 1h) 387 + 105 5 ; 1i) 112 − 64 3 ; 2a) 2; 2b) 5; 2c) 5y; 3a) 4a) 12 + 2 3 45 − 15 x ; 4b) 7 5 − 14 ; 4c) 33 9− x 35 ; 3b) 5 15 3x 2 ; 3c) ; 6 2