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Lesson 1

1. Lesson 1

1.6. Explore 2

Mathematics 20-1 Module 5

Module 5: Radicals

 

Try This 2

 

Consider the radical .

  1. Write the radicand as a product of two factors, , one of which is a perfect square. hint answer

  2. Simplify the result by evaluating the square root of the perfect square.

  3. Use your calculator to verify that the result is equal to .

  4. What other ways could you simplify ?

course folder Save your responses in your course folder.

 

Alternatives for Simplifying Entire Radicals

 

When an entire radical with a numerical radicand contains one or more perfect squares, there are two methods that can be used to express the radical as a mixed radical: a product of an integer and a radical. You may have used one of these methods in Try This 2.

 

Method 1: Factor Out the Greatest Perfect Square

 

 

Method 2: Completely Factor the Radicand into Prime Factors

 

 

In Discover you compared taking a root of a negative and of a positive radicand. “Simplifying Radicals” reviews the reason why you can take a root of a negative number if the index number is “odd.” How does this explanation compare with the general rule you created in Share 1?

 

This is a play button that opens “Simplifying Radicals.”

Khan Academy CC BY-NC-SA 3.0

The video also reviews how factoring the radicand helps to find the root of a large number without using a calculator. You can compare the strategy shown in the video with the one you used in Try This 2. Watch “Simplifying Radicals” now.



Self-Check 1
  1. Change the following entire radicals into mixed radicals using one method. Then check your answer using the other method. Which method works better for you?

    1. Answer

    2.  Answer

    3.  Answer

    4.  Answer

    5.  Answer

  2. For what values of the variables in question 1 parts c. and d. do the radicals represent real numbers? Answer
Try This 3

 

Now try the reverse process and change a mixed radical to an entire radical. Consider the radical .

  1. Write the coefficient as a square root. hint

  2. Multiply the two radicands together. hint

  3. Use your calculator to verify that the result is equal to .
Square the number and place the squared number within the radical symbol in order to write a number as a square root.
It is important to make sure you got the right answer. Did you get ?
is a perfect square since .