1. Squares, Square Roots and Perfect Squares

2. 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...

3. Click to see if the answer found with the Area formula is correct!
Area of a Square
The area (A) of a square can be found by squaring its side length, as shown below:
A = s2
Click to see if the answer found with the Area formula is correct!
A = 42 = 4 4
= 16 sq.units
The area (A) of a square is labeled as square units, or units2, because you cover the figure with squares...
4 units

4. What is the area of a square with sides of 5 inches?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
Answer: C

5. What is the area of a square with sides of 6 inches?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
Answer: D

6. If a square has an area of 9 ft2, what is the length of a side?3
If a square has an area of 9 ft2, what is the length of a side? A
2 ft B
2.25 ft C
3 ft D
4.5 ft
Answer: C

7. What is the area of a square with a side length of 16 in?4
What is the area of a square with a side length of 16 in?
Answer: 256 sq in

8. What is the side length of a square with an area of 196 square feet?5
What is the side length of a square with an area of 196 square feet?
Answer: 14 ft

9. When you square a number you multiply it by itself.
52 = = 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

10. Make a list of the numbers 1-15 and then square each of them.
Your paper should be set up as follows:
Number Square 3
(and so on)

11. Number Square
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.

12. Square
Root Square
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
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 = 9
What is 169?

13. Square Perfect
Root Square
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
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.

14. Find the following.
You may refer to your chart if you need to.

15. 6
What is ? 1
Answer: 1

16. 7
What is ? 81
Answer: 9

17. 8
What is the square of 15 ?
Answer: 225

18. 9
What is ?
256
Answer: 16

19. 10
What is 132?
Answer: 169

20. 11
What is ?
196
Answer: 14

21. 12
What is the square of 18?
Answer: 324

22. 13
What is 11 squared?
Answer: 121

23. 14
What is 20 squared?
Answer: 400

24. Squares of Numbers Greater than 20 Simplifying Perfect Squares
Day 13
Squares of Numbers Greater than 20
And
Simplifying Perfect Squares

25. Think about this...
What about larger numbers?
How do you find ?

26. What pattern do you notice?
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?
Teacher Instructions: Number in tens place squared, then two zeros are added

27. For larger numbers, determine between which two multiples of ten the number lies.
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100
Next, look at the ones digit to determine the ones digit of your square root.

28. Ends in nine so square root ends in 3 or 7 Try 53 then 57 532 = 2809
Examples:
Lies between 2500 & 3600 (50 and 60)
Ends in nine so square root ends in 3 or 7
Try 53 then 57
532 = 2809
Lies between 6400 and 8100 (80 and 90)
Ends in 4 so square root ends in 2 or 8
Try 82 then 88
822 = NO!
882 = 7744
2809
7744
Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

29. 15 Find. Answer: 28 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

30. 16 Find. Answer: 42 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100 42

31. 17 Find. Answer: 65 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

32. 18 Find. Answer: 48 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

33. 19 Find. Answer: 79 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

34. 20 Find. Answer: 99 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

35. 21 Find. Answer: 59 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

36. 22 Find. Answer: 47 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100

37. 23 Find. Answer: 101 Teacher Instructions: List of Squares
102 = = 1
202 = = 4
302 = = 9
402 = = 16
502 = = 25
602 = = 36
702 = = 49
802 = = 64
902 = = 81
1002 = = 100