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1-3 Real Numbers and the Number Line The radical symbol square root indicates a nonnegative 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 2 because 7 = 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 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 1 17 𝑎𝑛𝑑 4 3 What is an inequality that compares 129 𝑎𝑛𝑑 11.52 Problem 5: Graphing and Ordering Real Numbers 2 4, 0.4, − , 3 What is the order of 2, 𝑎𝑛𝑑 − 1.5 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 𝑎 , 𝑏 Rational Number: In the form 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 0.416 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