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Sect. 7.1 Radical Expressions & Radical Functions

Sect. 7.1 Radical Expressions & Radical Functions. Square Roots The Principal Square Root Square Roots of Expressions with Variables The Square Root Function Cube Roots The Cube Root Function Odd & Even n th Roots. Square Roots. Squaring a Number: 7 · 7 = 7 2 = 49

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Sect. 7.1 Radical Expressions & Radical Functions

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  1. Sect. 7.1 Radical Expressions & Radical Functions • Square Roots • The Principal Square Root • Square Roots of Expressions with Variables • The Square Root Function • Cube Roots • The Cube Root Function • Odd & Even nth Roots 7.1

  2. Square Roots Squaring a Number: 7·7 = 72 = 49 Squaring Negatives: (-7)·(-7) = (-7)2 = 49 The Square Roots = 7 of 49: = -7 7.1

  3. Simplifying square roots of numbers • Simplify each: (principal root only) 7.1

  4. Finding Function Values • Evaluate each function for a given value of x 7.1

  5. Square Roots of Variable Expressions 7.1

  6. The Square Root Function 7.1

  7. Cube Roots Cubing a Number: 7·7·7 = 73 = 343 Cubing Negatives: (-7)·(-7)·(-7) = (-7)3 = -343 The Cube Root of a positive number is positive The Cube Root of a negative number is negative 7.1

  8. Recognizing Perfect Cubes (X)3 • Why? You’ll do homework easier, score higher on tests. • Memorize some common perfect cubes of integers1 8 27 64 125 216 … 1000 13 23 33 43 53 63 … 103 • Unlike squares, perfect cubes of negative integers are different:-1 -8 -27 -64 -125 -216 … -1000 (-1)3 (-2)3 (-3)3 (-4)3 (-5)3 (-6)3 … (-10)3 • Flashback: Do you remember how to tell if an integer divides evenly by 3? • Variables with exponents divisible by 3 are also perfect cubesx3= (x)3y6= (y2)3-b15= (-b5)3 • Monomials, too, if all factors are also perfect cubesa3b15= (ab5)3 -64x18= (-4x6)3 125x6y3z51= (5x2yz17)3 7.1

  9. Examples to Simplify 7.1

  10. The Cube Root Function and its Graph Here is the basic graph: (8,2) ● (1,1) ● ● (0,0) ● (-1,-1) ● (-8,-2) 7.1

  11. Nth Roots 7.1

  12. Summary of Definitions 7.1

  13. Examples to Simplify 7.1

  14. What Next? • Present Section 7.2 7.1

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