Download Lesson 2 - Answers.notebook

Lesson 2 ­ Answers.notebook
September 11, 2014
Section 1.1 Square Roots of Perfect Squares
Some fractions and decimals can also be perfect squares.
If we can represent the area using squares than it is a
perfect square.
To determine if a fraction is a perfect square, we need
to find out if the numerator (top number) and the
denominator (bottom number) are both perfect squares.
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September 11, 2014
Fractions Examples
1. Is
a perfect square?
Since
and
then
is a perfect square.
Check your answer
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Lesson 2 ­ Answers.notebook
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This can also be represented by drawing a
diagram
using squares:
There are 2 out of 3 squares shaded along the width
and length of the square and there are 4 squares
shaded out of a total of 9 squares. And it still created
a square.
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2. Use a diagram to determine the value of
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Lesson 2 ­ Answers.notebook
3. Is
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a perfect square?
FIRST we must change this mixed number to an
improper fraction.
Remember multiply and add
+
x
to get the
numerator, the denominator
stays the same.
Are both the numerator (148) and denominator (9)
perfect squares?
No! 148 is not a perfect square therefore,
is not either.
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September 11, 2014
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Lesson 2 ­ Answers.notebook
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***NOTE*** Just because 16, 4, and 9 are
individually perfect squares, it did not necessarily
mean that
is automatically a perfect square
too. YOU MUST CHANGE TO IMPROPER
FRACTION to get the correct answer.
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4. Calculate the number whose square root is
Solution:
Complete the following examples in your exercise
book.....remember to include the section and date.
1. Calculate the number whose square root is:
A) B) C) D)
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2. Determine whether each fraction is a perfect square.
If it is calculate its square root. if its not a perfect
square state how you know.
A) B) C) D) E)
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September 11, 2014
Complete the following practice in your exercise book...
1. Use each diagram to determine the value of the square root.
A) B)
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2. Which numbers below are perfect squares? How do you know?
A)
B)
C)
D)
3. Calculate the number whose square root is:
A)
B)
C)
D)
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Lesson 2 ­ Answers.notebook
September 11, 2014
4. Determine the value of each square root.
A) B) C) D)
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Lesson 2 ­ Answers.notebook
September 11, 2014
Decimal Perfect Squares
Complete the patterns below....
Where does the decimal go?
Here‛s a hint...
•
if the perfect square is a whole number, than the square
root answer is smaller than the original number.
(9 is less than 81)
• if the perfect square is a rational number (decimal or
fraction) between 0 and 1, than the square root is bigger
than the original number.
(0.9 is greater than 0.81)
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September 11, 2014
In your exercise book make a list of Decimal Perfect Squares
by dividing all your Perfect Squares by 100 (move the decimal 2
places to the left)
Decimal Perfect Squares and their Square Roots
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Decimal Perfect Squares and their Square Roots
Perfect
Squares
Divide #s in
Column 1 by 100
1
1 ÷ 100 = 0.01
4
4 ÷ 100 = 0.04
9
9 ÷ 100 = 0.09
16
16 ÷ 100 = 0.16
25
25
÷ 100 = 0.25
36
36
÷ 100 = 0.36
49
49
÷ 100 = 0.49
64
64
÷ 100 = 0.64
81
81 ÷ 100 = 0.81
100
100
121
121 ÷ 100 = 1.21
144
144
169
169 ÷ 100 = 1.69
196
196 ÷ 100 = 1.96
225
225
÷ 100 = 2.25
256
256
÷ 100 = 2.56
289
289
÷ 100 = 2.89
324
324
÷ 100 = 3.24
361
361
÷ 100 = 3.61
400
400
÷ 100 = 4.00
Find Square Roots
of each # in Column 2
÷ 100 = 1.0
÷ 100 = 1.44
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To determine if a decimal is a perfect square,there are
a couple of ways to approach this question.
#1:
Change the decimal to a fraction and then
determine if the numerator and denominator are
perfect squares.
Yes,
is a perfect square.
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September 11, 2014
#2: Another way to complete this question is to
recognize that 12 x 12 = 144 and that
1.2 x 1.2 = 1.44, so 1.44 is a perfect square.
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Review how to change a decimal to a fraction
A) 0.6
The 6 is in the first decimal position called the
tenths place. Therefore,
B) 0.08
The 8 is in the second decimal position called the
hundredths place. Therefore,
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Lesson 2 ­ Answers.notebook
C) 0.25
The 5 is in the hundredths place.
September 11, 2014
Always look at the last
number and that's the
decimal position we
are looking for!
Therefore,
D) 0.379
The 9 is in the third decimal place called the
thousandths place. Therefore,
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Remember
0.1
=
1 (tenth)
10
0.01 =
1 (hundredth)
100
0.001 =
1000
1
0.0001 =
1
(thousandth)
(ten thousandth)
10 000
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Complete the following examples in your exercise
book...remember the date.
1. Use the diagram to determine the value of the
square root.
2. Which decimal is a perfect square 6.4 or 0.64?
Justify your answer.
6.4 is NOT a perfect square because it does NOT have an
EVEN amount of decimal places
* Also, the square root of 6.4 is non-terminating (does
not stop) and is non-repeating (does not have a pattern
such as 0.31313...)
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3. Calculate the number whose square roots is:
A) 1.21
B) 0.5
4. The area of a square is 51.84m2. Determine
the perimeter of the square.
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You can use a calculator to find out if a decimal is a perfect
square.
The square root of a perfect square decimal is either a
• terminating decimal (ends after a certain number of
decimal places)
or
• a repeating decimal (has a repeating pattern of digits in
the decimal).
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Lesson 2 ­ Answers.notebook
Decimal
September 11, 2014
Is decimal a Value of Square Type of Decimal
Root
perfect square?
1.69
1.3
terminating
yes
3.5
1.870 828 693
non­terminating
non­repeating
no
70.5
5.76
0.25
2.5
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Lesson 2 ­ Answers.notebook
Decimal
September 11, 2014
Value of Square Is decimal a Type of Decimal
perfect square?
Root
1.69
1.3
terminating
yes
3.5
1.870 828 693
non­terminating
non­repeating
no
70.5
8.396 427 811
non­terminating
non­repeating
no
5.76
2.4
terminating
yes
0.25
0.5
terminating
yes
2.5
1.581 138 830
non­terminating
non­repeating
no
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Lesson 2 ­ Answers.notebook
September 11, 2014
Complete the following practice in your exercise book...
1. Which numbers below are perfect squares?
How do you know?
A) 8.5
B) 2.89
C) 0.004
D) 0.0256
2.
Calculate the number whose square root is:
A) 0.6
B) 1.6
C) 0.92
D) 1.1
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Lesson 2 ­ Answers.notebook
September 11, 2014
3. Determine the value of each square root.
A)
B)
C)
D)
4. The area of a square garden is 12.25 m2.
A) Determine the perimeter of the garden.
B) The owner decides to put a gravel pathway around
the garden. This reduces the area of the garden
by 4.96 m2. What is the new side length of the
garden?
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Lesson 2 ­ Answers.notebook
September 11, 2014
FYI
When finding a square root, you find the number
that multiplies by itself.
because 9 x 9 = 81
What about -9? Can
because -9 x -9 = 81 ?
YES! Square roots can have negative answers, but
for us we will only be finding the principal square root
and that‛s the positive answer.
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