Squares, Square Roots and Perfect Squares. Area of a Square The area of a figure is the number of...
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Transcript of Squares, Square Roots and Perfect Squares. Area of a Square The area of a figure is the number of...
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...
A = 42 = 4 4
= 16 sq.units
Area of a Square
The area (A) of a square can be found by squaring its side length, as shown below:
Click to see if the answer found with the Area
formula is correct!
A = s2
4 units
The area (A) of a square is labeled as
square units, or units2, because you
cover the figure with squares...
1 What is the area of a square with sides of 5 inches?
A
B
D
C
16 in2
25 in2
20 in2
30 in2
2 What is the area of a square with sides of 6 inches?
16 in2
24 in2
20 in2
36 in2
A
B
D
C
3 If a square has an area of 9 ft2, what is the
length of a side?
A
B
D
C
2 ft
3 ft
2.25 ft
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.
52 = 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?
What is nine squared?
49
81
Make a list of the numbers 1-15 and then square each of them.
Your paper should be set up as follows:
Number Square 1 1 2 4 3
(and so on)
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 Square
1 12 43 94 165 256 367 498 649 8110
10011
12112
14413
16914
19615
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 Perfect Root Square
1 12 43 94
165
256
367
498
649
8110
10011
12112
14413
16914
19615
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 What is 132?
11 What is ?196
12 What is the square of 18?
13 What is 11 squared?
14 What is 20 squared?
Day 13Squares of Numbers
Greater than 20And
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.
102 = 100
202 = 400
302 = 900
402 = 1600
502 = 2500
602 = 3600
702 = 4900
802 = 6400
902 = 8100
1002 = 10000
What pattern do you notice?
For larger numbers, determine between which two multiples of ten the number lies.
102 = 100 1
2 = 1
202 = 400 2
2 = 4
302 = 900 3
2 = 9
402 = 1600 4
2 = 16
502 = 2500 5
2 = 25
602 = 3600 6
2 = 36
702 = 4900 7
2 = 49
802 = 6400 8
2 = 64
902 = 8100 9
2 = 81
1002 = 10000 10
2 = 100
Next, look at the ones digit to determine the ones digit of your square root.
2809
Examples:
Lies between 2500 & 3600 (50 and 60)Ends in nine so square root ends in 3 or 7Try 53 then 57
532 = 2809
Lies between 6400 and 8100 (80 and 90)Ends in 4 so square root ends in 2 or 8Try 82 then 88
822 = 6724 NO!
882 = 7744
7744
15 Find.
16 Find.
17 Find.
18 Find.
19 Find.
20 Find.
21 Find.
22 Find.
23 Find.