1. Section 10.1 Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

2. The number r is an nth root of x if denotes the principal nth root of x x is the _______________. is the _______________ symbol, or the radical. The natural number n is the _______________ or the order of the radical. 10.1 Lecture Guide: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions Radical Notation

3. Principal Square Root For any real number x > 0 AlgebraicallyVerballyNumericallyGraphically if and denotes the principal square root of x.

4. AlgebraicallyVerballyNumericallyGraphically if y is a real number and denotes the principal cube root of x. Principal Cube Root For any real number x:

5. Objective 1: Interpret and use radical notation.

6. Evaluate each expression. Use a calculator only to check your answer. 1.2.

7. Evaluate each expression. Use a calculator only to check your answer. 3.4.

8. Evaluate each expression. Use a calculator only to check your answer. 5.6.

9. Evaluate each expression. Use a calculator only to check your answer. 7.

10. Evaluate each expression. Use a calculator only to check your answer. 8.

11. Evaluate each expression. Use a calculator only to check your answer. 9.

12. Evaluate each expression. Use a calculator only to check your answer. 10.

13. Objective 2: Graph and analyze square root and cube root functions.

14. 11. Type: x-intercept: y-intercept: Domain: Range: Table Graph

15. 12. Type: x-intercept: y-intercept: Domain: Range: Table Graph

16. The domain of a real-valued function is the set of all real numbers for which is also a real number. This means the domain excludes all values that cause division by __________________ or cause a ___________________ number under a square root symbol. Domain of a Function

17. 13.Determine the domain of using a calculator. Then graph without a window of using by to verify your result.

18. 14.Determine the domain of using a calculator. Then graph without a window of using by to verify your result.

19. Determine the domain of the following. Use a graphing calculator only as a check on your work. 15.

20. Determine the domain of the following. Use a graphing calculator only as a check on your work. 16.

21. Determine the domain of the following. Use a graphing calculator only as a check on your work. 17.

22. Determine the domain of the following. Use a graphing calculator only as a check on your work. 18.

23. Determine the domain of the following. Use a graphing calculator only as a check on your work. 19.

24. Determine the domain of the following. Use a graphing calculator only as a check on your work. 20.

25. Match each function with the appropriate graph. Hint: Complete these problems by recognizing the shape of the graph from the defining equation. 21. ______ 22. ______ 23. ______ 24. ______ 25. ______ 26. ______

26. A.B.C. D.E.F. 21. ______

27. A.B.C. D.E.F. 22. ______

28. A.B.C. D.E.F. 23. ______

29. A.B.C. D.E.F. 24. ______

30. A.B.C. D.E.F. 25. ______

31. A.B.C. D.E.F. 26. ______

32. Mentally estimate the value of each expression and then use a calculator or a spreadsheet to approximate each value to the nearest thousandth. 27.28.

33. Mentally estimate the value of each expression and then use a calculator or a spreadsheet to approximate each value to the nearest thousandth. 29.30.

34. 31. Determine to the nearest tenth of a centimeter the length of the hypotenuse of a right triangle with legs of 5 cm and 7 cm. Use the formula

35. 32. Determine to the nearest tenth of a centimeter the radius of a sphere with a volume of Use the formula