1-3 Real Numbers and the Number Line

The radical symbol indicates a nonnegative square root

Problem 1: Simplifying Square Root Expressions

What is the simplified form of each expression

√81

Problem 1: Simplifying Square Root Expressions

What is the simplified form of each expression

√ 916

Problem 1: Simplifying Square Root Expressions

What is the simplified form of each expression

√64

Problem 1: Simplifying Square Root Expressions

What is the simplified form of each expression

√ 136

The square of an integer is called a perfect square. 49 is a perfect square because is a perfect square.

When a radicand is not a perfect square, you can estimate the square root.

Problem 2: 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 measures the area of one of the squares to be 386 square

microns. What is the approximate side of the square to the nearest micron?

Problem 2: Estimating a Square Root

What is the value of to the nearest integer

Problem 4: Comparing Real Numbers

Inequality: a mathematical sentence that compares the values of two expressions using an inequality symbol.< LESS THAN> GREATER THAN LESS THAN OR EQUAL TO GREATER THAN OR EQUAL TO

What is an inequality that compares

What is an inequality that compares

Problem 5: Graphing and Ordering Real Numbers

What is the order of from least to greatest. Then order on a number line.

Problem 5: Graphing and Ordering Real Numbers

What is the order of from least to greatest. Then order on a number line.

Problem 3: Classifying Real

Number

Rational Number: In the form , where a and b are integers and In decimal form they are terminating decimal such as 5.45 or a repeating decimal such as 0.416666… which you can write as

Natural numbers: also called counting numbers and are the ones you count with {1, 2, 3, …}

Whole Numbers: include the natural numbers, but also includes zero {0, 1, 2, 3, …}

Integers: The whole numbers, plus their respective negative numbers {…, -3, -2, -1, 0, 1, 2, 3, …}

Irrational numbers: cannot be written as a fraction. In decimal form, irrational numbers do not terminate or repeat.

(some square roots are rational and some are irrational)

(if a whole number is not a perfect square, its square is irrational ex:)

Rational numbers and irrational numbers form the set of Real numbers

To which subsets of the real number system does each number belong?• 15