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

9 16

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

1 36

The square of an integer is called a perfect square. 49 is a perfect square because 7 2 = 49 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 34 nearest integer to the

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 1 17 𝑎𝑛𝑑 4 3 What is an inequality that compares 129 𝑎𝑛𝑑 11.52

Problem 5: Graphing and Ordering Real Numbers

𝑎𝑛𝑑 − 1.5

2 What is the order of 4, 0.4, − , 2, 3 from least to greatest. Then order on a number line.

Problem 5: Graphing and Ordering Real Numbers

What is the order of 3.5, −2.1, 9, 7 − , 𝑎𝑛𝑑 5 from least to greatest. 2 Then order on a number line.

Problem 3: Classifying Real Number

Rational Number: In the form 𝑎 𝑏 , where a and b are integers and 𝑏 ≠ 0.

In decimal form they are terminating decimal such as 5.45 or a repeating decimal such as 0.416666… which you can write as 0.41 6

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: 3 = 1.73205080 … )

Rational numbers and irrational numbers form the set of Real

numbers

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

• 15 • −1.4583

• 57 • 3 10