1-3 REAL NUMBERS AND THE NUMBER LINEI Can:

- classify, graph, and compare real numbers .

- find and estimate square roots.

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.

SQUARE ROOT- You can use the definition of square

root to find the exact square roots of some nonnegative numbers.

- The radical symbol indicates a nonnegative square root, that is also called the principal square root.

VOCABULARY TO KNOW- Radicand

- The expression under the radical symbol is called the radicand.

- x is the radicand in this case

VOCABULARY TO KNOW

- Radical- Together, the radical symbol and

radicand form a radical.

SIMPLIFYING SQUARE ROOT EXPRESSIONS

- What is the simplified form of each expression?

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.

12 = 1 72 = 49

22 = 4 82 = 64

32 = 9 92 = 81

42 = 16 102 = 100

52 = 25 112 = 121

62 = 36 122 = 144

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 measured 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?

TYPES OF NUMBERS

- Numbers can be classified by their characteristics.

- Some can be represented on the number line.

SETS

- Numbers are classified using sets.- Set- a well-defined collection of

objects.- Each object is an element of the set.

- Subset- consists of elements from the given set.

Sets of Numbers

0natural numbers{1,2,3,…}

0whole numbers{0,1,2,3,…}

0Integers{…,-2,-1,0,1,2,…}

Sets of Numbers

4 5 6 7

51

3

11

2

5.75

• Rational numbers can be written in the form where a and b are integers. They can also be written in decimal form.• Decimals must be terminating or repeating.

3

Sets of Numbers

4 5 6 7

• Irrational numbers cannot be written in as a quotient of two integers.

• Decimals are non-terminating• Ex: 0.1010010001…, 3.141592…

3

15

#1 #2

integer, rational

What kind of number is 42?

What kind of number is -5?

natural, whole, integer, rational

#3What kind of number is -4.5669?

rational

#4Give an example of a whole number that isn’t positive.

REAL NUMBERS- Rational numbers and irrational numbers form the

set of real numbers.- Subsets of real numbers:

- Natural- Whole- Integer- Rational- Irrational

Inequalities

An inequality is a mathematical sentence comparing the values of two expressions using an inequality symbol.

0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9

8 -6>

Inequalities

0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9

-7 7<

#5-7 10

<

#6-5 + 10 10 - 5

=

ASSIGNMENT

- ODDS ONLY- P.20 #19-31, 41-47, 53-55, 63