Download Pre-AP Algebra 2 Unit 6 - Lesson 2 – Square Root

Pre-AP Algebra 2
Unit 6 - Lesson 2 – Square Root Equations
Learning Goal: The students will be able to solve radical equations. They will need to check their
answers for extraneous solutions
Guiding Questions: Why is your answer a “bad” answer if you came to it using correct Algebra? What
happens when you plug that answer back into the original problem?
How will we measure the learning goal?/Check for student understanding? Students will be assessed as
they participate in the class discussion and pairwork problems. Students will complete an exit ticket
problem.
15 min
Check for Understanding from last class
15 min
DO NOW
Students will review that solving equations is using inverse. (Comparing three problems)
Have students list out inverse operations:
Addition/subtraction
Multiplication/division
Squaring/square roots
Etc.
30 min
Direct Instruction
Background:
We solve equations by using inverse operations
Concepts:
Steps to solving square root functions
1. Isolate the radical term
2. Square both sides of the equation
3. Solve for the unknown(s)
4. Check for extraneous solutions
An extraneous solution is a solution that was found using correct algebra, but does not
satisfy the original equation.
Examples: Solve each equation for
1. √
2.
√
3. √
√
4. √
√
10 min
Pair Work
Students will work together to solve several radical equation.
Exit Ticket: Students will solve 2 equations
Homework # 6-2 – More practice if students need it
Pre-AP Algebra 2
Lesson 6-2 – DO NOW
Name__________________________
Compare how each of these 3 equations was solved. Why did I choose to make the steps I did?
3 x 2  2  10
3 x  7  11
3 x  7  7  11  7
3 x  18
3 x 18

3
3
x6
3 x 2  2  2  10  2
3 x 2  12
3 x 2 12

3
3
2
x 4
2( x  1)  3
3
5
 2( x  1)  3 
5
  5(3)
5


2( x  1)  3  15
2( x  1)  3  3  15  3
x2   4
x  2
2( x  1)  18
2( x  1) 18

2
2
x 1  9
x 8
Inverse Operations “undo” each other. Circle each time you see an inverse operation occur.
Make a list of pairs of inverse operations. Be prepared to share your answers.
Pre-AP Algebra 2
Lesson 6-2 – Pairwork
Name__________________________
Solve each equation.
1.
√
2. √
3. √
√
4. Solve the hull speed equation written in 6-1 Homework Problem #3.
5. Maggie claims that her 27-foot sailboat My Hero has a hull speed of 7 knots. The length
of her boat at the waterline is 24 feet. Is this claim reasonable? Explain why or why not.
Pre-AP Algebra 2
Lesson 6-2 – Homework
Name__________________________
Solve for x.
1. √
2. √
3. √
4. √
√
6. √
√
5. √
√
7. The radius of a circle is given by the formula
a. What is when
?
b. What is when
c. What is
when
?
√