 The
side length and area of a square
are related.
• The area is the square of the side length.
Example:
5 cm
5 cm
Area = (s)2 = 52 = 25 𝑐𝑚2
So, the area is 25 𝑐𝑚2
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• The side length is the square root of the area.
Example:
25 𝑐𝑚2
Area = 25 𝑐𝑚2
So, side = √ Area
= √25
= √5 x 5
= 5 cm
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FOCUS:
Find the square root of decimals and
fractions that are perfect squares.
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The square of a fraction or decimal is the
number multiplied by itself.
 Example:
4 2
( )
9
=
4
9
4
9
x =
16
81
(2.25)2 = 2.25 x 2.25 = 5.0625
16
81
So, and 5.0625 are perfect squares because they
are a product of 2 equal factors.
Therefore,
16
√
81
4
9
= and √5.0625 = 2.25
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 Finding
the Perfect Square Given Its Square
Root.
Example 1:
3
Calculate the number with the square root .
4
Solution:
3
4
x
3
4
=
9
16
3
4
So, is a square root of
Unit 1: Square Roots and Surface Area
9
16
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Example 2:
3
Calculate the number with square root .
2
Solution:
3
2
x
3
2
=
9
4
3
2
So, is a square root of
9
.
4
Example 3:
Calculate the number with square root 4.5.
Solution:
4.5 x 4.5 = 20.25
So, 4.5 is a square root of 20.25
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
Identifying Fractions That Are Perfect Squares.

Example 1:
Is the fraction
36
49
a perfect square? If so, find its square root.
Solution:
Check to see if the numerator and denominator are perfect
squares.
36 = 6 x 6, so 36 is a perfect square
49 = 7 x 7, so 49 is a perfect square
Therefore, 36/49 is a perfect square
Square root of
36
49
=
6
7
.
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 Example
2:
 Is the fraction
square root.
25
51
a perfect square? If so, find its
 Solution:
25 = 5 x 5, so 25 is a perfect square.
51 is not a perfect square since it is NOT the
product of 2 equal factors.
• Therefore,
25
51
is NOT a perfect square.
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
Identifying Decimals That Are Perfect Squares.

NOTE: The square root of a perfect square decimal is either
a terminating decimal or a repeating decimal.

Example 1:
Is the decimal 2.56 a perfect square?
Solution:
Use your calculator to find the square root.
So, √2.56 = 1.6, the square root is a terminating
decimal, therefore, 2.56 is a perfect square.
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Example
2: Is the decimal 4.5 a perfect
square?
Solution:
√4.5 = 2.121320344 …
The square root appears to be a decimal
that neither repeats or terminates.
So, 4.5 is NOT a perfect square.
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 HOMEWORK:
 Textbook:
Pages 11 to 13: #3, 4, 5, 7, 8, 9, 10,
11a, 13, 14, 15, 16, 17
 Workbook:
 Extra
page 7: Practice: #1, 2, 3, 4, 5, 6, & 7
Practice #1: #1, 2, 3, 4, 5, and 6
 Note:
#17 from Grade 8 Pythagorean Triples!!!!
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