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 n th Roots 7.11

2. Square Roots Squaring a Number: 7 · 7 = 7 2 = 49 Squaring Negatives: (-7)·(-7) = (-7) 2 = 49 The Square Roots = 7 of 49:= -7 7.12

3. Simplifying square roots of numbers  Simplify each: (principal root only) 7.13

4. Finding Function Values  Evaluate each function for a given value of x 7.14

5. Square Roots of Variable Expressions 7.15

6. The Square Root Function 7.16

7. Cube Roots Cubing a Number: 7 · 7 · 7 = 7 3 = 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 7.17

8. Recognizing Perfect Cubes (X) 3  Why? You’ll do homework easier, score higher on tests.  Memorize some common perfect cubes of integers 1 8 27 64 125 216 … 1000 1 3 2 3 3 3 4 3 5 3 6 3 … 10 3  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 cubes x 3 = (x) 3 y 6 = (y 2 ) 3 -b 15 = (-b 5 ) 3  Monomials, too, if all factors are also perfect cubes a 3 b 15 = (ab 5 ) 3 -64x 18 = (-4x 6 ) 3 125x 6 y 3 z 51 = ( 5x 2 yz 17 ) 3 7.18

9. Examples to Simplify 7.19

10. The Cube Root Function and its Graph Here is the basic graph: (8,2) ● (1,1) ● (0,0) ● (-1,-1) ● (-8,-2) 7.110

11. Nth Roots 7.111

12. Summary of Definitions 7.112

13. Examples to Simplify 7.113

14. What Next?  Present Section 7.2 Present Section 7.2 7.114