This document discusses squares and square roots. It defines what it means for a number to be squared or to find the square root. It explains that to square a number is to multiply it by itself, and the square root of a number is another number that when multiplied by itself gives the original number. The document provides examples of evaluating squares and square roots. It distinguishes between perfect squares, where the square root can be found exactly, and non-perfect squares, where the square root must be approximated.

1. and
Squares
SquareRoots

2. If a square measures 4
inches on each side, how
would you find its area?
4 inches4inches
4inches
4 inches

3. 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 non-
perfect squares

4. Why do we need to be able
to square and find the root
of a number?
• Squares and square roots are used in
the Pythagorean Theorem
• Squares and square roots are used
frequently in Algebra

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

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

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

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

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

10. What are exponents?
Remember multiplication is repeated
addition:
Exponents are repeated
multiplication:
4 x 5 = 4 + 4 + 4 + 4 + 4
45
= 4 x 4 x 4 x 4 x 4

11. What do the parts mean?
Tells you what to
multiply...
Tells you how
many...
= 5 x 5 x 5 x 5

12. Evaluate it!
= 5 x 5 x 5 x 5
B. 625A. 20

13. This is another formula for
finding the area of a square.
s
A = s2
s is the side
length

14. Evaluate it!
B. 49A. 14

15. Try these:
Number
Squared
Factors Standard
Form
92
11•11
9
102
9 • 9 81
112
121
32
3 • 3
10 • 10 100

16. Radicals (also called roots) are
directly related to exponents.

17. The simplest type of radical is a
square root.
Radicals beyond square roots
exist, but we will not explore
them here.

18. The rules for radicals that you
will learn work for all radicals –
not just square roots.

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

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

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

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

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

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

25. What does square root mean?

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

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

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

29. 49777 2
==⋅
Example:
because
Also
because
749 =
749 −= ( )( ) ( ) 49777
2
=−=−−

30. These numbers are called
perfect squares

31. 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.

32. What are the first 10 whole numbers
that are perfect squares?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
2222222222
10,9,8,7,6,5,4,3,2,1

33. Not all numbers have an exact
square root as in the previous
examples.

34. What if you are asked to
find the square root of a
non-perfect square?

35. Find the two closest perfect
squares.
16 = 4
The square root of 15
must be between 3 and 4,
closer to 4.
9 = 3

36. 20 would be between
which two whole numbers?
25 = 5
16 = 4
20
Between
4 and 5

37. Use the next process to find
a close approximation for
the square root of 10.

38. Is 10 a perfect square?
Can you make a square out of
these ten tiles?

39. Is 10 a perfect square?
Can you make a square out of
these ten tiles?

40. Can we approximate (get close
to) the square root of 10?
You have to make a square
out of the ten tiles

41. What is the length of each
side?
close !
Can we approximate (get close
to) the square root of 10?

42. 1
6Is 3 a good
approximation of 10 ?
1
63 = 3.1666666666666...
≈ 3.1622776601683...10

43. Most standardized tests
only ask for approximations
like this:
153 is between which of the following
consecutive whole numbers?
A. 15 and 16
B. 9 and 10
C. 12 and 13
D. 76 and 77

44. Quiz
1. Evaluate 72
2. Evaluate 144
3. Evaluate 33
4. 200 is between what
two consecutive whole
numbers?
49
12
27
14 and 15