Mini-Lecture 8.5: Solving Equations Containing Radicals | Montgomery College - Edubirdie

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

2023
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347

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1
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Tobsuchtbvow

Mini-Lecture 8.5 Solving Equations Containing Radicals Learning Objectives: 1. Solve radical equations by using the squaring property of equality once. 2. Solve radical equations by using the squaring property of equality twice. Examples: 1. Solve each equation. a) x =5 d) 2 x + 11 = 9 g) 5x − 2 = 2 x + 1 x − 3 = 13 b) e) 1 + y + 4 = 11 c) 3 x − 15 = 60 f) y+9 = y+3 h) x+8 − x = 2 i) 9 x 2 + 5 x − 20 = 3 x b) x − 27 = x − 3 c) x −1 = x − 9 f) x + 11 = 6 x − 9 2. Solve each equation. a) x + 3 = x + 21 Mixed Practice. Solve each equation. d) 5x − 1 = 3 e) x + 3 = 2 x + 7 Teaching Notes: • • • • Many students have to be reminded to isolate the radical before squaring both sides. Refer students to the textbook for To Solve a Radical Equation Containing Square Roots. Many students find the concept of extraneous solutions confusing. Show students a simple example of an extraneous solution, such as: x = 5 → square both sides → x 2 = 25 → x = ±5 → x = −5 is extraneous. • Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 25; 1b) 256; 1c) 625; 1d) not real; 1e) 96; 1f) 0; 1g) 1; 1h) 1; 1i) 4; 2a) 4; 2b) 36; 2c) 25; 2d) 2; 2e) 8; 2f) 4

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