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Math 84
Activity # 22
Your Name: ______________________
“Get Squared”
Part One: Overview and lesson:
The goal: To develop an understanding of the concept of square roots and perfect square numbers.
The Lesson
One: The square root of a number is a number that can be multiplied by itself to reach the initial number. For
example, the principal square root of 16 is 4, because 4x4=16, just as the principal square root of 36 is 6,
because 6 x 6 = 36.
For example.
25 = 5
5 is a square root of 25 because
Rule:
=
a2
5² = 25
b=
, then b a
The symbol used here is called the radical
sign (√), and it stands for the principal
square root of the number inside.
Two: Since the principal square root of 25 is the whole number (5), we refer to 25 as a perfect
square. A perfect square is a number which has a whole number as its principal square root.
Practice Problems:
1. A)
49 = ____
2. A)
121 =
because ____________
B)
64 = _____ because ___________
B)
25
=
81
3. Is 36 a perfect square? Why?________________________________________
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4. Circle the perfect square numbers:
68
144
9
12
169
189
225
4
25
27
16
You Try It: (Each member in your group must show the work on their own paper).
1.
103 +
49 =
2.
21 144 =
3.
64
=
100
4.
4
+
16
5.
Simplify.
6.
Check to see if the given number is a solution for the equation.
1
=
81
10 − 22 • 3 + 3
21 + 22
=______
A)
16 + x = 5,
B)
100
+ − x2
25
C)
125 − y = 11, y = 2 2
(
)
x = 9
= 10,
x = 3
New Vocabulary: Define the following.
1.
Radical __________________________________________
2.
Perfect Square ____________________________________
3.
Square root _______________________________________
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Review Problems
1. Gabriela is paid hourly and her hours vary week-to-week. Last month her four weekly
paychecks were as follow; $145, $230, $165 and $310. What was Gabriela’s mean weekly
salary?
2. A) Find the area of the rectangle.
B) Find the perimeter of the rectangle.
16m
3m
3. Simplify.
0
=
4
A)
B)
10 225
C)
4x + 2
=
0
D)
E)
103 + 49 =
8 − 2 • (10 − 1) + ( 32 + 4 • 3) =
4. Evaluate each expression for a = 20, b = 10, and c = 6.
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A) a + b + 2c =
B)
b+c =