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**Real Numbers and The Number Line**

Objectives Classify numbers and graph them on number lines. Tell which of two real numbers is less than the other. Find the additive inverse of a real number. Find the absolute value of a real number.

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Square Root A square root is one of two equal factors of a number. For example one square root of 64 is 8 since A number like 64, whose square root is a rational number is called a perfect square Example

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Square Root The symbol called a radical sign, is used to indicate the principal square root of the expression under the radical sign For example Note that is not the same as is not a real number since no real number multiplied by itself is negative

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Find Square Roots

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**Numbers that can not be expressed as rational numbers.**

Objective 1 Classify numbers and graph them on number lines NATURAL NUMBERS {1, 2, 3,…} WHOLE NUMBERS {0, 1, 2, 3,…} INTEGERS {…-2, -1, 0, 1, 2,…} RATIONAL NUMBERS Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals. Irrational numbers Numbers that can not be expressed as rational numbers.

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Real Numbers Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers The set of Real Numbers consists of the set of rational numbers and the set of irrational numbers.

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**Examples of Rational numbers**

5 - 7 0.3

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**EXAMPLES OF IRRATIONAL NUMBERS**

the is a whole number, but the , since It lies between 5 and 6,must be irrational.

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**Name the sets of numbers to which belongs.**

lies between 2 and 3 so it is not a whole number. Answer: irrational and real Name the sets of numbers to which belongs. Answer: natural , whole , integer , rational, and real Example 2-1c

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**a. b. c. d. Name the sets of numbers to which each number belongs.**

Answer: rational and real Answer: rational and real Answer: irrational and real Answer: natural , whole , integer rational and real (R) Example 2-1f

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**Answer: rational and real**

Answer: rational and real Answer: natural , whole , integer rational and real (R) Answer: irrational and real Answer: integer rational and real (R)

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**Completeness Property**

Each point on the number line corresponds to exactly one real number Example: Graph: ( -4, -2, 0, ,4, )

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**Objective 2 Tell which of two real numbers is less than the other**

Replace the with <, >, or = to make the sentence true. Since the numbers are equal. Answer: Example 7-4a

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**Objective 2 Tell which of two real numbers is less than the other**

Replace the with <, >, or = to make the sentence true. Answer: Example 7-4b

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**Objective 2 Order Real numbers from least to greatest**

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**Order Real numbers from least to greatest**

From the least to the greatest

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**Objective 3 Find the additive inverse of a real number.**

The opposite of 5 is The opposite of 5 is The opposite of -3 is When you add two opposite numbers , the sum is always 0.

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**Objective 4 Find the absolute value of a real number**

The absolute value of any number n is its distance from zero on a number line and is represented as Example: and 3 units 3 units

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END OF LESSON

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2-8 Square Roots and Real Numbers Objective: To find square roots, to classify numbers, and to graph solutions on the number line.

2-8 Square Roots and Real Numbers Objective: To find square roots, to classify numbers, and to graph solutions on the number line.

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