1. Real Numbers and the Number Line
The numbers in the pattern are integers and their squares.

2. Table of Perfect Squares
Integer
Perfect Square 1 2 3 4 5 6 7 8 9 10
Integer
Perfect Square 11 12 13 14 15 16 17 18 19 20

3. Real Numbers and the Number Line
A number a is a square root of a number b if a2 = b.
Example:
Together, the radical symbol and the radicand form a radical.

4. Problem 1
What is the simplified form of each expression?

5. Problem 2 Estimating a Square Root
The square of an integer is called a perfect square.
For example, 49 is a perfect square since
When a radicand is not a perfect square, you can estimate the square root.
Method 1: Estimate

6. Problem 2 Estimating a Square Root
Method 2: Estimate

7. 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.

8. The Real Numbers
Rational Numbers
Irrational Numbers
Real Numbers

9. Rational Numbers
The Rational Numbers have a subset called the integers.
The integers are the set
The Integers have a subset called the whole numbers.
The Whole Numbers are the set

10. Rational Numbers
The Whole Numbers have a subset called the natural numbers.
The Natural Numbers are the set
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.

11. Classifying Real Numbers

12. Problem 3 Classifying Real Numbers
To which subsets of the real numbers does each number belong to?

13. Inequality
An inequality is a mathematical sentence that compares the values of two expressions using an inequality symbol.
The inequality symbols are:

14. Problem 4 Comparing Real Numbers
What is an inequality that compares the following two numbers?

15. 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.