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DO NOW Friday, November 1, 2013
Please have Planners open with Homework and Signed Progress
Report on your desk.
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 square root 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 ExpressionAn exponential expression represents repeated multiplication.• Bases raised to an exponent of 2 are squared.
1. 92 2. 102
9 or -9 10 or -10
3. 4. PERFECT SQUARES25
814964
or - 59
59 or - 7
878
November 1, 2013
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 = 121√x2 = √112
x = 11
x = 11 and x = -11 both make the equation true.
(11)2 = 121 (-11)2 = 121
Solutions
1 separate (synonym)
Vocabulary
How many solutions will each of the following equations have?How do you know?
A y2 = 36
B y2 = 16
Explain why 7 are the solutions to the equation z2 = 49.
CFU
What can you say about the product of two numbers with the same sign (example: positive x positive)?
Each will have 2 solutions (+ and -)
1. a2 = 169 2. k2 = 225
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
981
a2 = 132
a = 13a = 13 and a = -13 both make the equation true.
132 = 169(-13)2 = 169
√a2 = √132
k2 = 152
k = 15k = 15 and k = -15 both make the equation true.
152 = 225(-15)2 = 225
√k2 = √152
q2 = ( )239
√q2 = √( )239
q = 39h = and h = - both make the equation true.
39
39
( )2 = 39
981
(- )2 = 39
981
p2 = ( )264
√p2 = √( )264
p = 64
h = and h = - both make the equation true.
64
64
( )2 = 64
3616
(- )2 = 64
3616
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
and so on…
3616
9
81
36
16
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. Jim’s family photo was placed in a frame. He knows the area of the picture frame is 196 in2. What is the length of each side of the frame?
_________________________________________________________________________________
6. Vanessa is framed a picture from her vacation. The area of the picture frame is 144 cm2. What is the length of each side of the frame?
_________________________________________________________________________________
s2 = 196s2 = 142
s = 14
142 = 196(-14)2 = 196
√s2 = √142
The length of each side of the tile is 14 in. (-14 in is not a solution because a length cannot be negative.)
Area = 121 in214 in
14 in
s2 = 144s2 = 122
s = 12
122 = 144(-12)2 = 144
√s2 = √122
The length of each side of the frame is 12 cm. (-12 cm is not a solution because a length cannot be negative.)
12 cm
12 cm
Sometimes Square Roots are not Integers, but instead fall between integers.
*
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
62 72 62 72
6 7
6 7
6 Why are estimates useful?
Do you think an estimate can be misleading? (Pair-Share)
CFU
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
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: ___________________11.1.13
481
19
1. g2 = 36 2. u2 = 169
3. c2 = 4. v2 =
Periodic Review 1
Access Common Core
1. p2 = 49 2. x2 = 225
3. b2 = 4. y2 =10025
25196
p = 7 x = 15
b = 105
y = 611
1. Choose Yes or No to indicate whether each statement is true about the equation p2 = 49.
A 49 is NOT a perfect square.B 49 divided by 2 = p.C p = 7 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 is smaller than 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
812
811
64121
Estimation
Approximately where does fall on the number line to the right?
75
25
25
196
100
64121
811
Name: __________________________11.1.13
Nam
e: _
____
____
____
____
____
____
_ 1
1.01
.13
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