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Roots Lesson #8 Pg. 231

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Simplify each expression. 1) 6² 36 2) 11 2 121 3) (–9)(–9) 81 4) 25 36 Write each fraction as a decimal. 5) 2525 5959 6) 7) 5 3838 8) –1 5656 0.4 5.375 0.5 –1.83 Warm Up

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Square Root/Cube Root Rational Numbers Perfect Square/Perfect Cube Irrational Numbers Natural Numbers Real Numbers Whole Numbers Repeating Decimal (Rational Number) Integers Terminating Decimal (Rational Number)Vocabulary Evaluate expressions containing square and cube roots. Classify numbers within the real number system. 2 equal factors multiplied together 3 equal factors multiplied together Index of 2Index of 3 ** Counting Numbers ** 1, 2, 3, 4, … ** Counting Numbers plus zero ** 0, 1, 2, 3, 4, … ** Natural, and Whole plus Negatives ** … - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, … ** Natural, Whole, Integers and any number that can be put into a ratio (fraction) * Repeating or Terminating decimals ** Non – Repeating, Non – Terminating decimals ** Any number (value) on the number-line

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

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What You’ll Learn Finding the square roots of perfect squares Finding the cube roots of perfect cubes Solving equations involving squares and cubes

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A square root of a number is one of its two equal factors Example 5 2 = 25, so 5 is the square root of 25 The radical symbol, is used to represent square roots. Positive real numbers have two square roots. 4 4 = 4 2 = 16 Square Roots = 4= 4 Positive square root of 16 (–4)(–4) = (–4) 2 = 16 = – 4 Negative square root of 16

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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 1212 1004 2 9 3232 16 4242 25 5252 36 6262 49 7272 64 8282 81 9292 10 2 The positive square root is represented by. The negative square root is represented by –. The positive and negative is represented by ±. Perfect Squares 400 20 2 361 19 2 121 11 2 144 12 2 169 13 2 196 14 2 225 15 2 256 16 2 289 17 2 324 18 2

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Examples

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Solving Examples

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Cube Roots A cube root of a number is one of it’s three equal factors Be careful, you can find the cube root of a negative under the radical Numbers such as 8, 27, and 64 are perfect cubes because they are the cubes of integers

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Examples

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Solving Examples

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HOMEWORK All Classes Pg. 235-236 1-23 all Test Corrections due Thursday

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Mrs.Volynskaya Real Numbers

Mrs.Volynskaya Real Numbers

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