8.1 Introduction to Radicals Prime Factorization and GCF

Warm Up Simplify each expression. 1. 6² 36 2. 112 121 25 36 3. (–9)(–9) 81 4. Write each fraction as a decimal. 2 5 5 9 5. 0.4 6. 0.5 5 3 8 –1 5 6 7. 5.375 8. –1.83

Vocabulary Objectives Evaluate expressions containing square roots. Square Root/Cube Root Rational Numbers Perfect Square Irrational Numbers Natural Numbers Real Numbers Whole Numbers Repeating Decimal Integers Terminating Decimal Objectives Evaluate expressions containing square roots. Classify numbers within the real number system.

The Real Number System Rational #s Irrational #s Every point (value) on the number line Rational #s Irrational #s Can be written as a ratio Decimal that repeats or ends Decimals that do not repeat or end Can not be written as a ratio Integers Tic marks on number line …-2, -1, 0, 1, 2… Whole #s 0, 1, 2, 3… Natural #s 1, 2, 3 …

Square Roots A number that is multiplied by itself to form a product is called a square root of that product. The operations of squaring and finding a square root are inverse operations. The radical symbol , is used to represent square roots. Positive real numbers have two square roots. 4  4 = 42 = 16 = 4 Positive square root of 16 (–4)(–4) = (–4)2 = 16 Negative square root of 16 – = –4

Perfect Squares The nonnegative square root is represented by . The negative square root is represented by – . A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table. 1 4 9 16 25 36 49 64 81 100 02 12 22 32 42 52 62 72 82 92 102

The expression Reading Math does not represent a real number because there is no real number that can be multiplied by itself to form a product of –36.

Finding Square Roots of Perfect Squares Find each indicated square root. A. Think: What number squared equals 16? 42 = 16 Positive square root positive 4. = 4 B. Think: What is the opposite of the square root of 9? 32 = 9 = –3 Negative square root negative 3.

Finding Square Roots of Perfect Squares Find the indicated square root. Think: What number squared equals ? 25 81 Positive square root positive . 5 9

Find the indicated square root. Try This! Find the indicated square root. 1a. 22 = 4 Think: What number squared equals 4? = 2 Positive square root positive 2. 1b. Think: What is the opposite of the square root of 25? 52 = 25 Negative square root negative 5.

Homework Pg. 527, 2 – 34 even Pg. 528, 48 – 54 even