What are we going to do? CFU Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with

What are we going to do?

CFU

Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with squared variables.

Make Connection

Evaluate the squared expressions.

We will solve equations with squared variables.

Learning Objective

Activate Prior Knowledge

62

base

exponent

Exponential ExpressionAn exponential expression represents repeated multiplication.• Bases raised to an exponent of 2 are squared.

1. 42 2. 72

16 49

3. (-4)2 4. (-7)2

16 49

Square Roots

Concept Development

A square root is a number that is multiplied by itself to form a product. • Taking the square root (√ ) is used to isolate1 the variable in equations

with squared variables.• An equation with squared variables can have two solutions, one

positive and one negative.Perfect Squares

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

x2 = 36√x2 = √62

x = 6

x = 6 and x = -6 both make the equation true.

(6)2 = 36 (-6)2 = 36

Solutions

1 separate (synonym)

Vocabulary

Which equation below can be solved by taking a square root?How do you know?

A y2 = 8

B y2 = 4

Explain why 3 are the solutions to the equation z2 = 9

CFU

1. a2 = 81 2. b2 = 25

3. h2 = 36 4. k2 = 16

5. q2 = 6. p2 =

7. w2 = 8. m2 =

Rewrite the numerical term as a squared expression.Solve the equation by taking the square root of both sides of the equation.Check and interpret2 the solution(s).

Solve equations with squared variables.1

23

2 explain (synonym)

Vocabulary

How did I/you solve the equation?How did I/you check and interpret the solution(s)?

CFU

2

3

Skill Development/Guided Practice

a2 = 92

a = 9a = 9 and a = -9 both make the equation true.

92 = 81(-9)2 = 81

√a2 = √92

b2 = 52

b = 5b = 5 and b = -5 both make the equation true.

52 = 25(-5)2 = 25

√b2 = √52

h2 = 62

h = 6h = 6 and h = -6 both make the equation true.

62 = 36(-6)2 = 36

√h2 = √62

k2 = 42

k = 4k = 4 and k = -4 both

make the equation true.

42 = 16(-4)2 = 16

√k2 = √42

A square root is a number that is multiplied by itself to form a product. • Taking the square root (√ ) is used to isolate the variable in equations with squared

variables.• An equation with squared variables can have two solutions, one positive and one negative.

Perfect Squares

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

q2 = 32

q = 3q = 3 and q = -3 both make the equation true.

32 = 9(-3)2 = 9

√q2 = √32

p2 = 102

p = 10p = 10 and p = -10 both make the equation true.

102 = 100(-10)2 = 100

√p2 = √102

w2 = 82

w = 8w = 8 and w = -8 both make the equation true.

82 = 64(-8)2 = 64

√w2 = √82

m2 = 72

m = 7m = 7 and m = -7 both make the equation true.

72 = 49(-7)2 = 49

√m2 = √72

9

64

100

49

Skill Development/Guided Practice (continued)

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

2

1

3

4

5

9. Cameron is tiling his floor with square tiles. He knows the area of each tile is 64 in2. What is the length of each side of the tile?

_________________________________________________________________________________

10. Vanessa is starting a painting on a square canvas. The area of the canvas is 81 in2. What is the length of each side of the canvas?

_________________________________________________________________________________

s2 = 64s2 = 82

s = 8

82 = 64(-8)2 = 64

√s2 = √82

The length of each side of the tile is 8 in. (-8 in is not a solution because a length cannot be negative.)

Area = 64 in28 in

8 in

Area = 81 in2

s2 = 81s2 = 92

s = 9

92 = 81(-9)2 = 81

√s2 = √92

The length of each side of the canvas is 9 in. (-9 in is not a solution because a length cannot be negative.)

9 in

9 in

Solving equations with squared variables will help you solve real-world problems.

Solving equations with squared variables will help you do well on tests.

1

Does anyone else have another reason why it is relevant to solve equations with squared variables? (Pair-Share) Why is it relevant to solve equations with squared variables? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?

CFU

2

Relevance



Sample Test Question:

87. Choose Yes or No to indicate whether each statement is true about the equation w2 = 4.

A The equation can be solved by taking a square root. B w = 16 C w = 2 D There are exactly two solutions to the equation.

O Yes O NoO Yes O NoO Yes O NoO Yes O No

How long is the Salinas River from King City to Soledad?

King City

Salinas River

Soledad

16 mi

12 mi The Salinas River is 20 miles long from King City to Soledad.

162 + 122 = r2

256 + 144 = r2

√400 = √r2

20 = r

What did you learn today about solving equations with squared variables? (Pair-Share)Use words from the word bank.

Access Common Core

Summary Closure

Word Bank

equationsquare root

solution

Rewrite the numerical term as a squared expression.Solve the equation by taking the square root of both sides of the equation.Check and interpret the solution(s).


23

Skill Closure

1. d2 = 49 2. n2 =

d2 = 72

d = 7d = 7 and d = -7 both


72 = 49

(-7)2 = 49

√d2 = √72

Which equation below can be solved by taking a square root? Explain your answer. Explain why the other equations cannot be solved by taking a square root.

A x2 = 25 B y2 = 16 C z2 = 13



Perfect Squares

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

n2 = 92

n = 9n = 9 and n = -9 both


92 = 81

(-9)2 = 81

√n2 = √92

81

Independent Practice

1. g2 = 36 2. u2 = 16

3. c2 = 1 4. v2 = 49

Rewrite the numerical term as a squared expression.Solve the equation by taking the square root of both sides of the equation.Check and interpret the solution(s).


23

g2 = 62

g = 6 g = 6 and g = -6 both make the equation true.

62 = 36

(-6)2 = 36

√g2 = √62

u2 = 42

u = 4 u = 4 and u = -4 both make the equation true.

42 = 16

(-4)2 = 16

√u2 = √42



Perfect Squares

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

c2 = 12

c = 1 c = 1 and c = -1 both make the equation true.

12 = 1

(-1)2 = 1

√c2 = √12

v2 = 72

v = 7 v = 4 and v = -4 both make the equation true.

72 = 49

(-7)2 = 49

√v2 = √72

Independent Practice (continued)

5. A square portion of Carmen’s apartment is tiled. Each tile is 1 ft2, and there are 25 tiles. How long is each side of the tiled portion of Carmen’s apartment?

_________________________________________________________________________________

s2 = 25s2 = 52

s = 5

52 = 25(-5)2 = 25

√s2 = √52

The length of each side of the tiled portion of Carmen’s apartment is 5 ft. (-5 ft is not a solution because a length cannot be negative.)

5 ft

5 ft

Periodic Review 1Extension:

Describe in your own words what it means to take the square root of a number:_______________________________________________________________________________________________________________________

How is squaring a number different from taking the square root of a number?_______________________________________________________________________________________________________________________

Periodic Review 1Extension:

Find the square of each number below:

Documents

What are we going to do? CFU Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with