Download 1.4 squares and square Roots

1.4
Squares and Square Roots
Lesson Objectives
Vocabulary
• Find a square of a number.
square (of a number)
base
square root
Le
• Find a square root of a perfect square.
exponent
perfect square
arn Find a square of a whole number.
a) A square has sides of length 8 centimeters.
Find the area of the square.
8 cm
Area of the square 5 8 3 8
5 64 cm2
8 3 8 is called the square of 8.
You can write 8 3 8 as 82.
82 is read as “8 squared”.
So, 82 5 64.
The number 2 in 82 is called the exponent.
The number 8 is called the base of the expression.
The square of a whole number is called a perfect square.
Since 64 5 8 3 8, 64 is a perfect square.
b)
Find the square of 5.
52 5 5 3 5
5 25
The square of 5 is 25.
I can relate this to finding the
area of a square with sides of
length 5 units.
5 units
Lesson 1.4 Squares and Square Roots
29
Guided Practice
Le
Find the square of each number.
1 2
2 6
3 9
4 11
arn Find a square root of a perfect square.
a)
A square has an area of 9 square inches. Find the length of each side of
the square.
Math Note
?
Area 5 9 in.2
You know that
Area of square 5 length 3 length.
To find the length of a side of the square, you need to find the number whose
square is 9.
Recalling the multiplication facts of 3, you know that
3 3 3 5 9.
So, the length of each side of the square is 3 inches.
3 is called a square root of 9. This can be written as
9 5 3.
You read this as “square root of 9 equals 3”.
Finding the square root of a
number is the inverse of finding
the square of a number.
30
The abbreviation in.2 is read
“square inches.”
Chapter 1 Positive Numbers and the Number Line
b)
Find the square root of 100.
I can relate this to finding the length
of the side of a square, given that it
has an area of 100 units2.
?
Area = 100 units2
Method 1
Recalling the multiplication facts of 10,
you know that
10 3 10 5 100
So,
100 5 10.
Method 2
By prime factorization,
100
2
2
·
50
2
·
2
·
25
·
2
·
5
·
100
5 2 · 2 · 5 · 5
5 (2 · 5) · (2 · 5)
5 (2 · 5)2
5 102
So,
5
Write the prime factorization.
Apply the Commutative Property of Multiplication.
Rewrite using an exponent.
100 5 10.
Guided Practice
Find the square root of each number.
5 25
6 64
7 144
8 196
Lesson 1.4 Squares and Square Roots
31
Practice 1.4
Find the square of each number.
1 3
2 7
3 12
4 10
Find the square root of each number.
5 36
6 81
7 121
8 49
Solve.
9 List the perfect squares that are between 25 and 100.
Find the value of each of the following.
10 352
11 562
12 642
13 289 14 400 15 484
Solve.
16 Given that 412 5 1,681, find the square of 410.
17 Given that 512 5 2,601, find the square root of 260,100.
18 Given that 676 5 26, evaluate 2, 704 .
19 Given that 1, 521 5 39, evaluate 3902.
20 Heather wants to make a giant quilt with sides of length 28 feet.
She uses square patches of fabric that have sides of length 4 feet.
How many patches of fabric will Heather need to make the giant quilt?
21 This week, customers at a carpet store pay $3 for a square foot of carpet.
Next week the store will be having a sale. During the sale, each square foot of
carpet will cost only $2. Neil wants to carpet two square rooms in his house.
The floor in one room is 10 feet by 10 feet. The floor in the other room is
14 feet by 14 feet. How much money will Neil save if he waits to buy carpet
during the sale?
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Chapter 1 Positive Numbers and the Number Line
4 ft
4 ft