1-3 Real Numbers and the Number Line
Objectives
To classify, graph, and compare real numbers
To find and estimate square roots
Dynamic Activity
Exploring Square Roots
The Real Number Line
Lesson Vocabulary
- square root
- radicand
- radical
- perfect square
- set
- element of a set
- subset
- rational numbers
- natural numbers
- whole numbers
- integers
- irrational numbers
- real numbers
- inequality
The diagrams in the Solve It model what happens when you multiply a number by itself to form a product. When you do this, the original number is called a square root of the product.
Take Note Key Concept: Square Root
Algebra A number a is a square root of a number b if
Example
Essential Understanding You can use the definition above to find the exact square roots of some nonnegative numbers. You can approximate the square roots of other nonnegative numbers.
The radical symbol
Together, the radical symbol and radicand form a radical. You will learn about negative square roots in Lesson 1–6.
Table of Contents
- 2-1 and 2-2 Solving One- and Two-Step Equations
- 2-3 Solving Multi-Step Equations
- 2-4 Solving Equations With Variables on Both Sides
- 2-5 Literal Equations and Formulas
- 2-6 Ratios, Rates, and Conversions
- 2-7 and 2-8 Solving Proportions and Using Similar Figures
- 2-9 Percents
- 2-10 Change Expressed as a Percent
- 3-1 Inequalities and Their Graphs
- 3-2 Solving Inequalities Using Addition or Subtraction
- 3-3 Solving Inequalities Using Multiplication or Division
- 3-4 Solving Multi-Step Inequalities
- 3-5 Working With Sets
- 3-6 Compound Inequalities
- 3-7 Absolute Value Equations and Inequalities
- 3-8 Unions and Intersections of Sets
- Chapter 1 Foundations for Algebra
- Chapter 2 Solving Equations
- Chapter 3 Solving Inequalities
- Chapter 4 An Introduction to Functions
- Chapter 5 Linear Functions
- Chapter 6 Systems of Equations and Inequalities
- Chapter 7 Exponents and Exponential Functions
- Chapter 8 Polynomials and Factoring
- Chapter 9 Quadratic Functions and Equations
- Chapter 10 Radical Expressions and Equations
- Chapter 11 Rational Expressions and Functions
- Chapter 12 Data Analysis and Probability