what are we going to do?

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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. 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. Learning Objective Activate Prior Knowledge 6 2 base exponent Exponential Expression An exponential expression represents repeated multiplication. Bases raised to an exponent of 2 are squared. 1. 9 2 2. 10 2 81 100 3. (-9) 2 4. (- 10) 2 81 100 PERFECT SQUARES

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Learning Objective. 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. What are we going to do?. CFU. Activate Prior Knowledge. An exponential expression represents repeated multiplication. - PowerPoint PPT Presentation

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Page 1: What are we going to do?

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.

1. We will solve equations with squared variables involving fractions.

2. We will estimate radicals that are not perfect squares.

Learning Objective

Activate Prior Knowledge

62

base

exponent

Exponential Expression

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

1. 92 2. 102

81 100

3. (-9)2 4. (-10)2

81 100

PERFECT SQUARES

Page 2: What are we going to do?

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 = 144√x2 = √122

x = 12

x = 12 and x = -12 both make the equation true.

(12)2 = 144 (-12)2 = 144

Solutions

1 separate (synonym)

Vocabulary

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

A y2 = 24

B y2 = 16

Explain why 7 are the solutions to the equation z2 = 49.

CFU

Page 3: What are we going to do?

1. a2 = 64 2. k2 = 144

3. q2 = 4. p2 =

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

925

a2 = 82

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

82 = 64(-8)2 = 64

√a2 = √82

k2 = 122

k = 12k = 12 and k = -12 both make the equation true.

122 = 144(-12)2 = 144

√k2 = √122

q2 = ( )235

√q2 = √( )235

q = 35h = and h = - both make the equation true.

35

35

( )2 = 35

925

(- )2 = 35

925 p2 = ( )27

4√p2 = √( )27

4p = 7

4

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

74

74

( )2 = 74

4916

(- )2 = 74

4916

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

4916

Page 4: What are we going to do?

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

5. Cameron is tiling his floor with square tiles. He knows the area of each tile is 121 in2. What is the length of each side of the tile?

_________________________________________________________________________________

6. Vanessa is starting a painting on a square canvas. The area of the canvas is 400 cm2. What is the length of each side of the canvas?

_________________________________________________________________________________

s2 = 121s2 = 112

s = 11

112 = 121(-11)2 = 121

√s2 = √112

The length of each side of the tile is 11 in. (-11 in is not a solution because a length cannot be negative.)

Area = 121 in211 in

11 in

Area = 400 cm2

s2 = 400s2 = 202

s = 20

202 = 400(-20)2 = 400

√s2 = √202

The length of each side of the canvas is 20 cm. (-20 cm is not a solution because a length cannot be negative.)

20 cm

20 cm

Page 5: What are we going to do?

Sometimes Square Roots are not Integers, but instead fall between integers.

1

How can you estimate a square root of a number that is not a perfect square ? (Pair-Share)

Square roots can have how many solutions?

CFU

Relevance

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

4964

72 82 72 82

7 8Between 7 and 7.5

Page 6: What are we going to do?

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).

Solve equations with squared variables.1

23

Skill Closure

1. d2 = 49 2. n2 =

d2 = 72

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

make the equation true.

72 = 49

(-7)2 = 49

√d2 = √72

2581

n2 = ( )259

√n2 = √( )259

n = 59

n = and n = - both make the equation true.

59

59

( )2 = 59

2581

(- )2 = 59

2581

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 x = 49 B y2 = 16

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

25

81

Page 7: What are we going to do?

Independent Practice

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).

Solve equations with squared variables.1

23

481

19

g2 = 62

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

62 = 36

(-6)2 = 36

√g2 = √62

u2 = 132

u = 13 u = 13 and u = -13 both make the equation true.

132 = 169

(-13)2 = 169

√u2 = √132

c2 = ( )229

√c2 = √( )229

c = 29

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

29

29

( )2 = 29

481

(- )2 = 29

481

v2 = ( )213

√v2 = √( )213

v = 13

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

13

13

( )2 = 13

19

(- )2 = 13

19

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

Name: ___________________10.31.13

481

19

1. g2 = 36 2. u2 = 169

3. c2 = 4. v2 =

Page 8: What are we going to do?

Periodic Review 1

Access Common Core

1. p2 = 1 2. x2 = 64

3. b2 = 4. y2 =1

2536

121

p = 1 x = 8

b = 15

y = 611

1. Choose Yes or No to indicate whether each statement is true about the equation p2 = 9.

A The equation cannot be solved by taking a square root. B p = 81 C p = 3 D There is more than one solution to the equation.

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

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

A The equation cannot be solved by taking a square root. B w = - C w = D There are exactly two solutions to the equation.

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

328116

94

Estimation

Approximately where does fall on the number line to the right?

38

25

36

121

1