Squares, Square Roots and
Perfect Squares
Area of a Square
The area of a figure is the number of square units needed to
cover the figure.
The area of the square below is 16 square units because 16 square
units are needed to COVER the figure...
Area of a Square
The area (A) of a square can be found by squaring its side length, as
shown below:
2
A=s
2
A=4 =4 4
Click
see if the
= 16tosq.units
answer found
4 units
with
the Area
formula is
correct!
The area (A) of a square is labeled as
2
square units, or units , because you
cover the figure with squares...
1
What is the area of a square with sides of 5
inches?
A
16 in2
B
20 in2
C
25 in2
D
30 in2
2
What is the area of a square with sides of 6
inches?
A
16 in2
B
20 in2
C
24 in2
D
36 in2
3
2
If a square has an area of 9 ft , what is the
length of a side?
A
2 ft
B
2.25 ft
C
3 ft
D
4.5 ft
4
What is the area of a square with a side length
of 16 in?
5
What is the side length of a square with an
area of 196 square feet?
When you square a number you multiply it by itself.
2
5 =5
5 = 25 so the square of 5 is 25.
You can indicate squaring a number with an exponent of 2, by asking
for the square of a number, or by asking for a number squared.
What is the square of seven?
49
What is nine squared?
81
Make a list of the numbers 1-15 and then square each of them.
Your paper should be set up as follows:
Number
1
2
3
(and so on)
Square
1
4
Number Square
1
1
2
4
3
9
4
16
5
25
6
36
7
49
8
64
9
81
10
100
11
121
12
144
13
169
14
196
15
225
The numbers in the right column are
squares of the numbers in the left column.
If you want to "undo" squaring a number,
you must take the square root of the
number.
So, the numbers in the left column are the
square roots of the numbers in the right
column.
Square
Root
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Square
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
The square root of a number is found by
undoing the squaring. The symbol for
square root is called a radical sign and it
looks like this:
Using our list, to find the square root of a
number, you find the number in the right
hand column and look to the left.
So, the 81 = 9
What is 169?
Square
Root
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Perfect
Square
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
When the square root of a number is a
whole number, the number is called a
perfect square.
Since all of the numbers in the right
hand column have whole numbers for
their square roots, this is a list of the
first 15 perfect squares.
Find the following.
You may refer to your chart if you need to.
6
What is
1 ?
7
What is
81?
8
What is the square of 15 ?
9
What is
256 ?
10
2
What is 13 ?
11
What is
196?
12
What is the square of 18?
13
What is 11 squared?
14
What is 20 squared?
Day 13
Squares of Numbers
Greater than 20
And
Simplifying Perfect
Squares
Think about this...
What about larger numbers?
How do you find
?
It helps to know the squares of larger numbers such as the multiples
of tens.
2
102 = 100
20 = 400
2
302 = 900
402 = 1600
502 = 2500
602 = 3600
702 = 4900
802 = 6400
90 2= 8100
100 = 10000
What pattern do you notice?
For larger numbers, determine between which two multiples of ten
the number lies.
2
102 = 100
202 = 400
302 = 900
402 = 1600
502 = 2500
602 = 3600
702 = 4900
802 = 6400
90 2= 8100
100 = 10000
2
12
22
32
42
52
62
72
82
9
= 1
= 4
= 9
= 16
= 25
= 36
= 49
= 64
= 2 81
10 = 100
Next, look at the ones digit to determine the ones digit of your
square root.
Examples:
2809
Lies between 2500 & 3600 (50 and 60)
Ends in nine so square root ends in 3 or 7
Try2 53 then 57
53 = 2809
7744
Lies between 6400 and 8100 (80 and 90)
Ends in 4 so square root ends in 2 or 8
Try2 82 then 88
822 = 6724 NO!
88 = 7744
15
Find.
16
Find.
17
Find.
18
Find.
19
Find.
20
Find.
21
Find.
22
Find.
23
Find.