1 3 REAL NUMBERS AND THE NUMBER LINE

1 -3 REAL NUMBERS AND THE NUMBER LINE I 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 a 2 = 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

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 natural numbers {1, 2, 3, …} 0 whole numbers {0, 1, 2, 3, …} 0 Integers {…, -2, -1, 0, 1, 2, …} 0

Sets of Numbers 3 4 5 6 7

Sets of Numbers 3 4 5 6 • Irrational numbers cannot be written in as a quotient of two integers. • Decimals are non-terminating • Ex: 0. 1010010001…, 3. 141592… 7

#1 What kind of number is -5? integer, rational #2 What kind of number is 42? natural, whole, integer, rational

#3 What kind of number is -4. 5669? rational

#4 Give 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. -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 8 > -6

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

#5 -7 < #6 -5 + 10 10 = 10 - 5

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