1. 1-3 Real Numbers and the Number Line

2. The radical symbol indicates a nonnegative square root

3. Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression 81

4. Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression
9 16

5. Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression 64

6. Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression
1 36

7. The square of an integer is called a perfect square
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.

8. 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?

9. Problem 2: Estimating a Square Root
What is the value of to the nearest integer

10. 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

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

12. Problem 5: Graphing and Ordering Real Numbers
What is the order of 4 , 0.4, − 2 3 , 2 , 𝑎𝑛𝑑 −1.5 from least to greatest. Then order on a number line.

13. Problem 5: Graphing and Ordering Real Numbers
What is the order of 3.5, −2.1, 9 , − 7 2 , 𝑎𝑛𝑑 5 from least to greatest. Then order on a number line.

14. Problem 3: Classifying Real Number

15. Rational Number: In the form 𝑎 𝑏 , where a and b are integers and 𝑏≠0
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 … which you can write as

16. 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, …}

17. Irrational numbers: cannot be written as a fraction
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 = …)

18. Rational numbers and irrational numbers form the set of Real numbers

20. To which subsets of the real number system does each number belong?15
−1.4583 57
3 10