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1-5 ROOTS
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Squares Square of a number: “Squaring” a number means to raise a number to the second power. Example: 4² = 4 · 4 = 16 9² = 9 · 9 = 81 16² = 16 · 16 = 256
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Square Roots The Square Root of a number is the number you can multiply by itself to give you that number. Thus, = 2, because 22=4 = 3, because 32=9 Try: = 8, because 82=64 = 12, because 122=144 = 1, because 12 = 1 = 0, because 02 = 0
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WHAT IS THE RELATIONSHIP BETWEEN SQUARING A NUMBER AND TAKING THE SQUARE ROOT?
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Square Roots UNDO Squares
INVERSE OPERATIONS = =
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Perfect Squares MEMORIZE THEM 25 81 1 36 100 4 49 121 9 144 16 64
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POSITIVE AND NEGATIVE SQUARE ROOT
Every number has a positive AND negative square root. ± Example Usually only the positive square root is considered. When solving an equation you must include ± because both the positive and negative are the correct answer. Example Solve
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SQUARE ROOT OF NEGATIVE NUMBER
vs. There is no real square root because nothing times itself is going to give you a -16.
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EXAMPLES
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A. 1. B. 2. C. 3. D. 4.
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Cubes Cube of a number: “Cubing” a number means to raise a number to the third power. = 2 · 2 · 2 = 8 =5 · 5 · 5 = 125
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Cube Roots The Cube Root of a number is the number you can multiply by itself twice to give you that number.
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WHAT IS THE RELATIONSHIP BETWEEN CUBING A NUMBER AND TAKING THE CUBE ROOT?
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Cube Roots UNDO Cubes INVERSE OPERATIONS = =
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Perfect Cubes MEMORIZE THEM 1 27 8 125 64
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CUBE ROOT OF A NEGATIVE NUMBER
vs.
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A. B. C.
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