Math 10C Module 2 Lesson 4

Module 2: Roots and Powers

 

Lesson 4: Mixed and Entire Radicals

 

Focus

This shows a photo of a laptop computer chained shut and locked down.

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In this lesson you will learn how to simplify radicals. You use radicals when you apply the Pythagorean theorem. In Module 1 you solved surface area and volume problems that involved the use of radicals. Solving other equations in mathematics may also involve radicals.

 

Like the irrational numbers you learned about in Lesson 3, radicals can be used in the creation of secret codes. In fact, a cipher has been developed to improve the security of e-mails. A computer scientist named Michael Rabin developed a system that uses the squaring of numbers to convert plaintext to ciphertext to keep the contents secret. For decryption, he uses radicals!

Outcomes

At the end of this lesson, you will be able to demonstrate an understanding of radicals by

  • expressing a radical as a mixed radical in simplest form
  • expressing a mixed radical as an entire radical
  • explaining, using examples, the meaning of the index of a radical
  • ordering a set of radicals on a number line

Lesson Questions
  • How are mathematical processes reversed?
  • How can the properties of radicals be used to simplify and order irrational numbers?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Assess tab or by using the Quizzes link under the Activities block.


** Note – Share questions may have to be done on your own depending on your learning situation**

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