The document discusses classifying, graphing, and comparing real numbers, including finding and estimating square roots. It defines real numbers as numbers that can be located on the number line, including integers, rational numbers, and irrational numbers. The document also discusses the differences between finding the square root of a perfect square versus a non-perfect square.

1. 1-3 Real Numbers and
the Number Line
I Can:
- classify, graph, and compare real
numbers .
- find and estimate square roots.

2. 1. Opener
Simplify each of these:
a) ( 1 1 1 1 1 1 1)( 1)( 1
)( )( )( )( )( )( )(50)
b) ( 2)(3)( 4)(5)
c) 10 ( 32) ( 22)
d) 
1 2 3 4  50
e) x 2 5x 6
Evaluate: for x = 6
f) What number could you evaluate in (e) so that x2 5x 6 0
g) What appetizer is most requested with a last meal?

3. Focus Question
• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?

4. Vocabulary to Know
• Square Root
• A number a is a square root of a number b if a2 = b
• Example: 72 = 49, so 7 is the square root of 49.

5. Square Root
• You can use the definition of square root to find the exact square roots of some
nonnegative numbers.
• You can approximate the square roots of other nonnegative numbers.
• The radical symbol indicates a nonnegative square root, that is also called the
principal square root.

6. Vocabulary to Know
• Radicand
• The expression under the radical symbol is called the radicand.
• x is the radicand in this case

7. Vocabulary to Know
• Radical
• Together, the radical symbol and radicand form a radical.

8. BIG Ideas
• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.

9. BIG Ideas
• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.

10. BIG Ideas
• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
• Numbers can be classified by their characteristics.

11. BIG Ideas
• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
• Numbers can be classified by their characteristics.
• Some types of numbers can be represented on the number line.

12. Simplifying Square Root Expressions
•

13. Simplifying Square Root Expressions
•

14. Vocabulary to Know
• Perfect Square
• The square of an integer

15. Vocabulary to Know
• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.

16. Vocabulary to Know
• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.
• Copy this list and study it. You will be quizzed.
12 = 1 72 = 49
22 = 4 82 = 64
32 = 9 92 = 81
42 = 16 102 = 100
52 = 25 112 = 121
62 = 36 122 = 144

17. Estimating a Square Root
• Lobster eyes are made of tiny square regions. Under a microscope, the surface
of the eye looks like graph paper. A scientist measure the area of one of the
squares to be 386 square microns. What is the approximate side length of the
square of the nearest micron?

18. Estimating Square Root
•

19. Focus Question Answer
• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?

20. Focus Question
• Why is it helpful to classify, graph, and compare numbers?

21. 2. Kinds of Numbers
natural numbers
0
whole numbers
0
integers
0

22. 2. Kinds of Numbers
1
11
5 5.75
3
2
3 4 5 6 7 8
rational numbers

23. 2. Kinds of Numbers
15
3 4 5 6 7 8
irrational numbers

24. #1
What kind of number is -
5?

25. #1
What kind of number is -
#2
What kind of number is
5? 42?
integer, rational

26. #2
What kind of number is
#3
What kind of number is -
42? 4.5669?
natural, whole, integer,
rational

27. #3
What kind of number is -
#4
Give an example of a
4.5669? positive integer.
rational

28. #4
Give an example of a
#5
Give an example of a
positive integer. negative natural
number.

29. #5
Give an example of a
#6
Give an example of a
negative natural whole number that isn’t
number. positive.

30. #6
Give an example of a
#7
What kind of number is
whole number that isn’t most useful to describe:
positive.
your shoe size

31. #7
What kind of number is
#8
What kind of number is
most useful to describe: most useful to describe:
your shoe size the temperature in a
news report
rational

32. #8
What kind of number is
#9
What kind of number is
most useful to describe: most useful to describe:
the temperature in a the number of siblings a
news report person has
integers

33. #9
What kind of number is
#10
True or false:
most useful to describe:
Every rational number is
the number of siblings a also an integer.
person has
If false, give a
counterexample.
whole

34. #10
True or false:
#11
True or false:
Every rational number is Every whole number is
also an integer. also a natural number.
If false, give a If false, give a
counterexample. counterexample.
false

35. #11
True or false:
#12
True or false:
Every whole number is Every natural number is
also a natural number. also a rational number.
If false, give a If false, give a
counterexample. counterexample.
false

36. #12
True or false:
#13
True or false:
Every natural number is Every negative number
also a rational number. is also an integer.
If false, give a If false, give a
counterexample. counterexample.
true

37. #13
True or false:
Every negative number
is also an integer.
If false, give a
counterexample.
true

38. 2. Kinds of Numbers
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
8 >
-6

39. 2. Kinds of Numbers
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-7 <
7

40. #14
-7 10
<

41. #14
-7 10
#15
-5 + 10 10 - 5
<

42. #15
-5 + 10 10 - 5
#16
10 • 22 2 • 42
=

43. #16
10 • 22 2 • 42
>

44. Graphing and Ordering Real Numbers
• http://www.phschool.com/atschool/academy123/english/academy123_conten
t/wl-book-demo/ph-483s.html

45. Focus Question Answer
• Why is it helpful to classify, graph, and compare real numbers?

46. Your Assignment
• Pages 23-25
• 1-5
• 9-17 odd
• 18-34 even
• 35-47 odd
• 48
• 49-59 odd
• 60-64 even
• 66-79