1. a
qu
S
s
re
and Sq
uar
Roo e
ts

2. We will:
• Understand the meaning of squaring a
number and finding the square root of a
number
• Find squares of numbers
• Raise a whole number to a whole number
power
• Find square roots of perfect squares
• Find approximate square roots of nonperfect squares

3. Shade in graph paper to make each of the shapes below. Each shape is a
square.
Count and write the number of square tiles in each of the
larger squares below.
1.
2.
3.

4. Continue to draw larger squares. Make one that is 7 tiles
wide and 7 tiles high; then make one that is 8 wide and 8
high. Count the number of squares in each shape.
4. 7 by 7 = ____
5. 8 by 8 = ____

5. Talk to the person next to you about the following
questions. Be prepared to discuss them if I call on you.
•The numbers 1, 4, 9, 16, 25, etc. are known as perfect
squares. Why do you think they are called perfect squares?
•How are the width and the height of the squares related?
How are they related to the total number of tiles?
•How could you find the next numbers that are perfect
squares without tiles?

6. If a square measures 4
inches on each side, how
would you find its area?
4 inches
4 inches
4 inches
4 inches

7. Remember how to
calculate the area?
4 inches
4 inches
A=l•w
A = 4 in. • 4 in.
A = 16 in.
2

8. A square must have the
same length and width.
4 inches
4 inches
A=l•w
A = 4 in. • 4 in.

9. Square Number
• Also called a “perfect square”
• A number that is the square
of a whole number
• Can be represented by
arranging objects in a square.

10. Square Numbers

11. To square a number means
to multiply it by itself.
5 squared means 5 x 5
Take the number 5
And square it!

12. There is a shorter way to
write 5 x 5.
Say:
“5 squared” or
“5 to the 2nd power”.

13. These are the parts.
This is the
base
This is the
exponent

14. This is another formula for
finding the area of a square.
s
A=s
2
s is the side
length

15. Evaluate it!
A. 14
B. 49

16. Try these:
Number
Squared
2
9
11
2
3
2
10
2
Factors Standard
Form
9 • 9
11•
11
3 • 3
10 • 10
81
121
9
100

17. These numbers are called
perfect squares

18. If a number is a perfect square, then you
can find its exact square root.
A perfect square is simply a number that
can be written as the square of another
number.

19. What are the first 10 whole numbers
that are perfect squares?
2
2
2
2
2
2
2
2
2
1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
2

20. -What’s the opposite operation to
addition?
-What’s the opposite operation to
multiplication?
-The opposite operation to squaring
a number is taking the square root.
62 = 36
36 = 6

21. The symbol used to indicate a
root is the radical symbol -

22. Every radical expression has
three parts…
• Radical symbol
• Index
• Radicand

23. Every radical expression has
Radical
three parts…
Index
2
49
Radicand

24. The index of a radical is a whole
number greater than or equal to
2.

25. The index of a square root is
always 2.

26. The square root of 49 could
2
be written as 49 …
but is normally written as 49 .

27. What does square root mean?

28. The square root of a number is another
number which when multiplied by itself
gives back the original number.

29. What is a square root?
?
the measure of the
side of the square
16 = 4

30. What is the square root
of 36?
36 = 6

31. Example:
49 = 7
because
7 ⋅ 7 = 7 = 49
2
Also
49 = − 7 because ( − 7 )( − 7 ) = ( − 7 ) = 49
2

32. Find the two square roots of each number.
A. 49
–
49 = 7
49 = –7
B. 100
100 = 10
– 100 = –10
7 is a square root, since 7 • 7 = 49.
–7 is also a square root, since
–7 • –7 = 49.
10 is a square root, since 10 • 10 = 100.
–10 is also a square root, since
–10 • –10 = 100.

33. Find the two square roots of each number.
A. 25
–
25 = 5
25 = –5
B. 144
144 = 12
5 is a square root, since 5 • 5 = 25.
–5 is also a square root, since
–5 • –5 = 25.
12 is a square root, since 12 • 12 = 144.
– 144 = –12 –12 is also a square root, since
–12 • –12 = 144.

34. Open your books to page 72 so we
can try some problems together