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**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

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Square Roots Vocabulary & Notes

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**Vocabulary Objectives square root rational numbers**

perfect square irrational numbers real numbers repeating decimal natural numbers terminating decimal whole numbers Integers Objectives Evaluate expressions containing square roots. Classify numbers within the real number system.

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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

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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

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**The expression does not represent**

a real number because there is no real number that can be multiplied by itself to form a product of –36. Reading Math

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**Finding Square Roots of Perfect Squares**

Find each 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.

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**Finding Square Roots of Perfect Squares**

Find the square root. Think: What number squared equals ? 25 81 Positive square root positive 5 9

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**Find the square root. 1a. 22 = 4 = 2 1b. 52 = 25**

Try This! Find the 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.

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