Mastering Radical Equations: Square Root Method

1. Objective: The students will take notes on how to Solve Equations by Taking Square Roots. Students will demonstrate their understanding by achieving an accuracy rate of 70% or higher on my.hrw.com assignment Monday. CFU: What are we going to learn TODAY? Math Notebook & Whiteboard

2. Activate Prior Knowledge Inverse Operations Inverse operations are operations that undo each other. Solve simple quadratic equations. Students, you already know the inverse operation of squaring is taking the square root. Now, we will use the inverse operation of squaring and taking the square root to solve simple radical equations. Make Connection

3. Concept Development • A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived1 solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. CFU Solving Radical Equations radical Square both sides of the equation radical Solve the quadratic equation Derived solutions Check each derived solution: 1 obtained from a sequence of steps Vocabulary True False

4. Skill Development/Guided Practice (continued) • A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. How did I/you isolate the square root onto one side of the equation? How did I/you solve for the variable? How did I/you check for extraneous solutions? CFU Solve simple radical equations. 1 Isolate the square root onto one side of the equation. Square both sides of the equation. Solve for the variable. Hint: Solving will be different for linear and quadratic expressions. Check for extraneous solutions by substituting each derived solution into the equation. 1 2 3 3 4 4 ( )2 ( )2 ( )2 ( )2 x – 7 = 64 x = 71 Check Check

5. Skill Development/Guided Practice (continued) • A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. How did I/you isolate the square root onto one side of the equation? How did I/you solve for the variable? How did I/you check for extraneous solutions? CFU Solve simple radical equations. 1 Isolate the square root onto one side of the equation. Square both sides of the equation. Solve for the variable. Hint: Solving will be different for linear and quadratic expressions. Check for extraneous solutions by substituting each derived solution into the equation. 1 2 3 3 4 4 ( )2 ( )2 ( )2 ( )2 Check Check

6. Independent Practice (continued) • A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. Solve simple radical equations. Isolate the square root onto one side of the equation. Square both sides of the equation. Solve for the variable. Hint: Solving will be different for linear and quadratic expressions. Check for extraneous solutions by substituting each derived solution into the equation. 1 2 3 4 ( )2 ( )2 ( )2 ( )2 Check Check

7. Skill Development/Guided Practice (continued) Solving Math Problems 1 Determine what the question is asking. 2 Determine the math concept required. 3 Determine relevant information. 4 Solve the problem, then interpret the answer. 5 Check the reasonableness of your answer. How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 4 Identify all the radical equations where extraneous solutions occur when solving. Solve to confirm whether extraneous solutions exist or not. 5 Solving Math Problems 1 What am I trying to find? 2 What do I know about this idea? 3 What amounts do I know? 4 Solve the problem or answer the question. 5 Did I answer all parts of the question? This equation does not have extraneous solutions.

8. Relevance • A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. Solving simple radical equations will help you in an engineering career. 1 Solving simple radical equations will help you do well on a test. 2 Does anyone else have another reason why it is relevant to solve simple radical equations? (Pair-Share) Why is it relevant to solve simple radical equations? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU

9. A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. Skill Closure Solve simple radical equations. Isolate the square root onto one side of the equation. Square both sides of the equation. Solve for the variable. Hint: Solving will be different for linear and quadratic expressions. Check for extraneous solutions by substituting each derived solution into the equation. 1 2 3 4 Word Bank ( )2 ( )2 ( )2 ( )2 Check Check

10. A radical equation is an equation where a variable is inside a radical sign. • An extraneous solutionof an equation is a derived solution which does not satisfy the equation. • To check for extraneous solutions, substitute each derived solution into the equation to see if it satisfies the equation. • An extraneous solution can occur in solving a radical equation when there is a variable outside of the radical sign. Access Common Core Word Bank Word Bank radical square root extraneous derived solution Summary Closure What did you learn today about solving simple radical equations? (Pair-Share) Use words from the word bank.

11. Periodic Review 1 Solving Math Problems 1 What am I trying to find? 2 What do I know about this idea? 3 What amounts do I know? 4 Solve the problem or answer the question. 5 Did I answer all parts of the question? Solve simple radical equations. No Solution Access Common Core Create two radical equations with one solution. Then solve each equation to confirm there only exists one solution for each. Answers will vary. However, a correct answer will have equations where there is not an additional variable outside the radical sign, and when the radical is isolated, the other side is a positive constant. Answering ELA Questions 1 Determine what the question or prompt is asking. 2 Determine the ELA concept required. 3 Read the text to determine relevant information. 4 Answer the question. 5 Re-read the directions to determine if you answered all parts of the question.

12. Periodic Review 2 Solving Math Problems 1 What am I trying to find? 2 What do I know about this idea? 3 What amounts do I know? 4 Solve the problem or answer the question. 5 Did I answer all parts of the question? Solve simple radical equations. Access Common Core Create two radical equations with no solutions. Then solve each equation to confirm solutions do not exist. Answers will vary. However, a correct answer will have equations where when the radical is isolated, there is a negative number on the other side of the equation. Answering ELA Questions 1 Determine what the question or prompt is asking. 2 Determine the ELA concept required. 3 Read the text to determine relevant information. 4 Answer the question. 5 Re-read the directions to determine if you answered all parts of the question.

13. Periodic Review 3 Solving Math Problems 1 What am I trying to find? 2 What do I know about this idea? 3 What amounts do I know? 4 Solve the problem or answer the question. 5 Did I answer all parts of the question? Solve simple radical equations. Access Common Core Create two radical equations where extraneous solutions may occur. Then solve each equation to confirm whether there are extraneous solutions. Answers will vary. However, a correct answer will have equations which have an additional variable outside of the radical. Answering ELA Questions 1 Determine what the question or prompt is asking. 2 Determine the ELA concept required. 3 Read the text to determine relevant information. 4 Answer the question. 5 Re-read the directions to determine if you answered all parts of the question.