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Mastering Radical Expressions: A Comprehensive Guide to Addition, Subtraction, and Multiplication

This lesson focuses on understanding and simplifying radical expressions using various techniques, including rational exponents and radical forms. Students will learn how to add, subtract, multiply, and divide radicals, emphasizing the importance of having like terms. Through engaging examples and interactive group challenges, students will explore practical applications in geometry. The session concludes with a quiz to reinforce knowledge and assess understanding, ensuring learners can confidently work with radical expressions.

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Mastering Radical Expressions: A Comprehensive Guide to Addition, Subtraction, and Multiplication

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  1. Expressions with Radicals March 14th, 2013 PI DAY!!! 3-14

  2. Warm Up 1. Rewrite using rational exponents: 2. Rewrite in radical form then simplify the radical: 3. Simplify:

  3. Homework Solutions

  4. Do you see a pattern?

  5. Do you see a pattern?

  6. Summarize: Adding/Subtracting Radicals • In order to add/subtract radicals, the _____________ must be the same. • To add/subtract radicals, simply add/subtract the________________.

  7. Examples:

  8. You Try

  9. What about this?

  10. You Try

  11. How can we use this in geometry? • Find the perimeter of the rectangle below in radical form:

  12. You Try: • Find the perimeter of the square below in radical form:

  13. Do you see a pattern?

  14. ]Summarize:Multiplying Monomial Radicals • To multiply monomial radicals (radicals that only have one term), multiply their “outsides” together then multiply their “insides” together

  15. Examples: • Don’t forget to simplify the product, when possible!

  16. You Try: • Don’t forget to simplify the product, when possible.

  17. How would we multiply this? (x + 6)(3x – 1)

  18. So how do you think we should multiply this???

  19. Examples:

  20. You Try:

  21. Geometry applications • Find the area of the following rectangle:

  22. Find the area of the following triangle:

  23. You Try: • Find the area of the square and triangle below:

  24. Homework • WORKBOOK • P. 295 (1-17 odd)

  25. Warm Up

  26. Homework Solutions

  27. Amigo Bingo • Fill in your board with your classmates’ names below:

  28. Complete the problems on the sheet that I assign. We will check in after every few questions to mark names off of our board.

  29. Quiz – Adding, Subtracting, and Multiplying Radical Expressions • You may use your notes, but not your neighbors.

  30. Dividing Radicals • How can we simplify these?

  31. Dividing Radicals

  32. You Try:

  33. Rationalizing • We can never leave a radical in the denominator of a fraction. (This makes mathematicians cringe and is not considered simplified.) • In order to get rid of a radical in the denominator, we have to “rationalize” the denominator. • In other words, we need to get the “rat” (radical) out of the “den” (denominator).

  34. How can we get rid of a radical? • What operation cancels radicals? • What is ?

  35. How can we rationalize (get rid of the radical) here? • Are we allowed to just randomly multiply the denominator by something? • What are we allowed to multiply by without changing the problem (think IDENTITY PROPERTY OF MULTIPLICATION)?

  36. Examples:

  37. You Try:

  38. Examples: • Don’t forget to simplify your final answers!

  39. You Try:

  40. Examples with variables: • Don’t forget to simplify your final answers.

  41. You Try:

  42. THINK/PAIR/SHARE • What does it mean to rationalize a fraction? THINK silently for 30 seconds. PAIR discussion with your partner for 30 seconds. SHARE with the class.

  43. TEAM CHALLENGE!!! • Work with your group to create a radical expression that needs to be simplified (it can involve addition, subtraction, multiplication, division, or a combination of these). • Make sure you know how to simplify it correctly. Simplify your expression on a separate sheet of paper.

  44. TEAM CHALLENGE!!! • You will have the opportunity to challenge another team to simplify your expression. • If they simplify it correctly, they will earn 3 points. If they simplify it incorrectly, your team will earn a point. You will then have the opportunity to challenge another team with your problem, so every team should be working on the problem (even if you were not challenged).

  45. TEAM CHALLENGE!!! • If no one simplifies your expression correctly after 3 rounds, we will go on to another problem. • If you stump Ms. Freiberg, you will earn 5 points!!!

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