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Perfect Squares

Perfect Squares

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Perfect Squares

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  1. Perfect Squares 64 225 1 81 256 4 100 289 9 121 324 16 144 25 361 169 400 36 196 49 625

  2. Simplify = 2 = 4 This is a piece of cake! = 5 = 10 = 12

  3. Radicals Students are expected to: * Demonstrate an understanding of the role of irrational numbers in applications. * Approximate square roots. * Demonstrate an understanding of and apply properties to operations involving square roots. * Apply the Pythagorean Theorem. * Use inductive and deductive reasoning when observing patterns, developing properties, and making conjectures.

  4. A Radical is the root of a number. What are radicals?

  5. A Radical is the root of a number. What are radicals?

  6. A Radical is the root of a number. What are radicals? coefficient radical

  7. For example: A Radical is the root of a number. What are radicals? radical sign coefficient radical

  8. A Radical is the root of a number. For example: What are radicals? coefficient radical

  9. A Radical is the root of a number. For example: 5 is the square root of 25 because 5x5 = 25 What are radicals? coefficient radical

  10. A Radical is the root of a number. For example: 5 is the square root of 25 because 5x5 =25 What are radicals? coefficient radical

  11. A Radical is the root of a number. For example: 5 is the square root of 25 because 5x5 = 25 2 is the cubed root of 8 because 2x2x2 = 8. What are radicals? coefficient radical

  12. You can determine the root using mental math. Determining Roots

  13. You can determine the root using mental math. Example: Determining Roots

  14. You can determine the root using mental math. Example: Determining Roots

  15. You can determine the root using mental math. Example: You can also find the root using your calculator. Determining Roots

  16. You can determine the root using mental math. Example: You can also find the root using your calculator. Example: Determining Roots

  17. You can determine the root using mental math. Example: You can also find the root using your calculator. Example: Determining Roots

  18. You can determine the root using mental math. Example: You can also find the root using your calculator. Example: Be careful not to hit the wrong button on your calculator! Determining Roots

  19. Let’s investigate! 1)

  20. 2)

  21. 3) I. Solve for the hypotenuse of the different triangles in your geoboard paper. • II. At the back of your paper, draw a square with an area of: • 34 • 41 • 52 • 29

  22. Simplifying Square Roots

  23. Perfect Square Factor * Other Factor Simplify = = = = LEAVE IN RADICAL FORM = = = = = =

  24. Perfect Square Factor * Other Factor Simplify = = = = LEAVE IN RADICAL FORM = = = = = =

  25. Perfect Square Factor * Other Factor Simplify = = = = LEAVE IN RADICAL FORM = = = = = =

  26. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals

  27. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals Example 1:

  28. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals Example 1:

  29. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals Example 1: Example 2:

  30. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals Example 1: Example 2:

  31. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals Example 1: Example 2: Example 3:

  32. Only like radicals can be added or subtracted. Like radicals can have different coefficients as long as the radicals are the same. Subtract the coefficients but keep the same radical. You may have to simplify your question first, to get a like radical. Adding and Subtracting Radicals Example 1: Example 2: Example 3:

  33. One common mistake is adding without having like radicals. Common Mistakes Made While Adding and Subtracting Radicals

  34. One common mistake is adding without having like radicals. Common Mistakes Made While Adding and Subtracting Radicals

  35. One common mistake is adding without having like radicals. Always make sure that the radicals are similar. Common Mistakes Made While Adding and Subtracting Radicals

  36. One common mistake is adding without having like radicals. Always make sure that the radicals are similar. Another common mistake is forgetting to simplify. Common Mistakes Made While Adding and Subtracting Radicals

  37. One common mistake is adding without having like radicals. Always make sure that the radicals are similar. Another common mistake is forgetting to simplify. Common Mistakes Made While Adding and Subtracting Radicals

  38. One common mistake is adding without having like radicals. Always make sure that the radicals are similar. Another common mistake is forgetting to simplify. This question is not done! The answer is: Common Mistakes Made While Adding and Subtracting Radicals

  39. Multiplying Radicals Steps Example:

  40. Multiplying Radicals Steps Example:

  41. Multiply coefficients together Multiplying Radicals Steps Example: 1.

  42. Multiply coefficients together Multiply radicals together Multiplying Radicals Steps Example: 1. 2.

  43. Multiply coefficients together Multiply radicals together Simplify radicals if possible Multiplying Radicals Steps Example:

  44. Correct example: Examples of Multiplying Radicals

  45. Correct example: Examples of Multiplying Radicals

  46. Correct example: Examples of Multiplying Radicals

  47. Correct example: Be careful to multiply the coefficients with coefficients and radicals with radicals. Examples of Multiplying Radicals

  48. Incorrect Example: Correct example: Be careful to multiply the coefficients with coefficients and radicals with radicals. Examples of Multiplying Radicals