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10.3 Simplifying Radical Expressions

10.3 Simplifying Radical Expressions. Objective 1 . Use the product rule for radicals. Slide 10.3- 2. Use the product rule only when the radicals have the same index. Use the product rule for radicals. Slide 10.3- 3. CLASSROOM EXAMPLE 1. Using the Product Rule. Solution:.

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10.3 Simplifying Radical Expressions

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  1. 10.3 Simplifying Radical Expressions

  2. Objective 1 Use the product rule for radicals. Slide 10.3- 2

  3. Use the product rule only when the radicals have the same index. Use the product rule for radicals. Slide 10.3- 3

  4. CLASSROOM EXAMPLE 1 Using the Product Rule Solution: Multiply. Assume that all variables represent positive real numbers. Slide 10.3- 4

  5. CLASSROOM EXAMPLE 2 Using the Product Rule Solution: Multiply. Assume that all variables represent positive real numbers. This expression cannot be simplified by using the product rule. Slide 10.3- 5

  6. Objective 2 Use the quotient rule for radicals. Slide 10.3- 6

  7. Use the quotient rule for radicals. Slide 10.3- 7

  8. CLASSROOM EXAMPLE 3 Using the Quotient Rule Solution: Simplify. Assume that all variables represent positive real numbers. Slide 10.3- 8

  9. Objective 3 Simplify radicals. Slide 10.3- 9

  10. Be careful with which factors belong outside the radical sign and which belong inside. Simplify radicals. Slide 10.3- 10

  11. CLASSROOM EXAMPLE 4 Simplifying Roots of Numbers Solution: Simplify. Cannot be simplified further. Slide 10.3- 11

  12. CLASSROOM EXAMPLE 5 Simplifying Radicals Involving Variables Solution: Simplify. Assume that all variables represent positive real numbers. Slide 10.3- 12

  13. CLASSROOM EXAMPLE 6 Simplifying Radicals by Using Smaller Indexes Solution: Simplify. Assume that all variables represent positive real numbers. Slide 10.3- 13

  14. Simplify radicals. Slide 10.3- 14

  15. Objective 4 Simplify products and quotients of radicals with different indexes. Slide 10.3- 15

  16. CLASSROOM EXAMPLE 7 Multiplying Radicals with Different Indexes Solution: Simplify. The indexes, 2 and 3, have a least common index of 6, use rational exponents to write each radical as a sixth root. Slide 10.3- 16

  17. Objective 5 Use the Pythagorean theorem. Slide 10.3- 17

  18. Use the Pythagorean theorem. Slide 10.3- 18

  19. The length of the hypotenuse is CLASSROOM EXAMPLE 8 Using the Pythagorean Theorem Solution: Find the length of the unknown side of the triangle. c2 = a2 + b2 c2 = 142 + 82 c2 = 196 + 64 c2 = 260 Slide 10.3- 19

  20. The length of the leg is CLASSROOM EXAMPLE 8 Using the Pythagorean Theorem (cont’d) Solution: Find the length of the unknown side of the triangle. c2 = a2 + b2 62 = 42 + b2 36 = 16 + b2 20 = b2 Slide 10.3- 20

  21. Objective 6 Use the distance formula. Slide 10.3- 21

  22. Use the distance formula. Slide 10.3- 22

  23. CLASSROOM EXAMPLE 9 Using the Distance Formula Find the distance between each pair of points. (2, –1) and (5, 3) Designate which points are (x1, y1) and (x2, y2). (x1, y1) = (2, –1) and (x2, y2) = (5, 3) Solution: Start with the x-value and y-value of the same point. Slide 10.3- 23

  24. Find the distance between each pairs of points. (–3, 2) and (0, 4) Designate which points are (x1, y1) and (x2, y2). (x1, y1) = (–3, 2) and (x2, y2) = (0, 4) CLASSROOM EXAMPLE 9 Using the Distance Formula (cont’d) Solution: Slide 10.3- 24

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