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Section 9.1

Section 9.1. Finding Roots. Find the square root of a number. A. Square a radical expression. B. OBJECTIVES. Classify the square root of a number and approximate it with a calculator. C. OBJECTIVES. Find higher roots of numbers. D. Solve an application involving square roots. E.

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Section 9.1

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  1. Section 9.1 Finding Roots

  2. Find the square root of a number. A Square a radical expression. B OBJECTIVES

  3. Classify the square root of a number and approximate it with a calculator. C OBJECTIVES

  4. Find higher roots of numbers. D Solve an application involving square roots. E OBJECTIVES

  5. DEFINITION Square Root If a is a positive real number,

  6. DEFINITION Square Root

  7. RULE Squaring a Square Root When the square root of a non-negative real number a is squared, the result is that positive real number:

  8. RULE Square Root of aNegative Number

  9. Chapter 9 Roots and Radicals Section 9.1Exercise #1

  10. Find.

  11. Chapter 9 Roots and Radicals Section 9.1Exercise #2

  12. Find the square of each radical expression.

  13. Chapter 9 Roots and Radicals Section 9.1Exercise #3

  14. Classify each number as rational, irrational, or not a real number, and simplify if possible.

  15. Chapter 9 Roots and Radicals Section 9.1Exercise #4

  16. Find each root, if possible.

  17. Chapter 9 Roots and Radicals Section 9.1Exercise #5

  18. A diver jumps from a cliff 20 meters high. If the time t (in seconds) it takes an object dropped from a distance d (in meters) to reach the ground is given by: How long does it take the diver to reach the water? The diver takes 2 seconds.

  19. Section 9.2 Multiplication and Division of Radicals

  20. Multiply and simplify radicals using the product rule. A OBJECTIVES

  21. Divide and simplify radicals using the quotient rule. B OBJECTIVES

  22. Simplify radicals involving variables. C OBJECTIVES

  23. Simplify higher roots. D OBJECTIVES

  24. Product Rule for Radicals If a and b are nonnegative numbers,

  25. Quotient Rule for Radicals If a and b are positive numbers,

  26. Absolute Value for Radicals For any real number a,

  27. Properties of Radicals For all real numbers where the indicated roots exist,

  28. Chapter 9 Roots and Radicals Section 9.2Exercise #6

  29. Simplify.

  30. Chapter 9 Roots and Radicals Section 9.2Exercise #7

  31. Multiply.

  32. Chapter 9 Roots and Radicals Section 9.2Exercise #8

  33. Simplify.

  34. Chapter 9 Roots and Radicals Section 9.2Exercise #9

  35. Simplify.

  36. Chapter 9 Roots and Radicals Section 9.2Exercise #10

  37. Simplify.

  38. Section 9.3 Addition and Subtractions of Radicals

  39. Add and subtract like radicals. A OBJECTIVES

  40. Use the distributive property to simplify radicals. B OBJECTIVES

  41. Rationalize the denominator in an expression. C OBJECTIVES

  42. PROCEDURE Rationalizing Denominators Method 1: Multiply both numerator and denominator of the fraction by the square root in the denominator.

  43. PROCEDURE Rationalizing Denominators Method 2: Multiply numerator and denominator by the square root of a number that makes the denominator the square root of a perfect square.

  44. Chapter 9 Roots and Radicals Section 9.3Exercise #11

  45. Simplify.

  46. Chapter 9 Roots and Radicals Section 9.3Exercise #12

  47. Simplify.

  48. Chapter 9 Roots and Radicals Section 9.3Exercise #13

  49. Simplify.

  50. Chapter 9 Roots and Radicals Section 9.3Exercise #14

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