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Real Numbers and the Number Line The numbers in the pattern are integers and their squares. Table of Perfect Squares Integer Perfect Square Integer 1 2 3 11 12 13 4 5 6 14 15 16 7 17 8 9 18 19 10 20 Perfect Square Real Numbers and the Number Line A number a is a square root of a number b if a2 = b. Example: 7 49, so 7 is a square root of 49 2 or 49 7. Together, the radical symbol and the radicand form a radical. Problem 1 What is the simplified form of each expression? A. 81 C. 9 16 B. 25 D. 1 36 Problem 2 Estimating a Square Root The square of an integer is called a perfect square. For example, 49 is a perfect square since 7 49 2 When a radicand is not a perfect square, you can estimate the square root. Method 1: Estimate 86 by finding the two closest perfect squares. Problem 2 Estimating a Square Root Method 2: Estimate 86 by using a calculator. Estimate 375 to the nearest integer using both methods? Classifying Real Numbers You can classify numbers using sets. A set is a well-defined collection of objects. Each object is called an element of the set. A subset of a set consists of elements from the larger set. You can list elements of a set within braces {}. The set of Real Numbers is the largest set of numbers that you will work with. It is divided into two subsets: the Rational Numbers and the Irrational Numbers. The Real Numbers Rational Numbers a , where a and b are integers and b 0 b Real Numbers Irrational Numbers cannot be written as the quotient of two integers Rational Numbers The Rational Numbers have a subset called the integers. The integers are the set ...,2,1,0,1,2,3,... The Integers have a subset called the whole numbers. The Whole Numbers are the set 0,1,2,3,... Rational Numbers The Whole Numbers have a subset called the natural numbers. The Natural Numbers are the set 1,2,3,4,... Some square roots are rational numbers and some are irrational numbers. If a whole number is not a perfect square, then its square root is irrational. Classifying Real Numbers Problem 3 Classifying Real Numbers To which subsets of the real numbers does each number belong to? A. 15 B. 3 4 C. 1.4583 D. 12 Inequality An inequality is a mathematical sentence that compares the values of two expressions using an inequality symbol. The inequality symbols are: Problem 4 Comparing Real Numbers What is an inequality that compares the following two numbers? A. 1 17 and 4 3 B. 129 and 11.52 Problem 5 Graphing and Ordering Real Numbers Order the following set of numbers from least to greatest. Note: To perform this task, you can write every number as a decimal rounded to the nearest hundredth, and then graph each of the numbers on a number line. Then, read the graph from left to right. 7 3.5, 2.1, 9, , and 2 5