Lesson 1
1. Lesson 1
1.7. Explore 3
Module 5: Radicals
Example: Changing a Mixed Radical to an Entire Radical
Change 
to an entire radical.
Step 1: Begin by expressing the coefficient, 6, as a square root because the radical is a square root. Square 6 and put the resulting number under a square-root sign.
Step 2: Check by computing the values for the original question and the answer using a calculator.
Note that only positive radicands are used in the examples because square roots of negative radicands would not be real numbers, as you demonstrated in the Discover section. Negative radicands, however, could be used for radicals with an odd index number, such as cube roots.
Self-Check 2
Convert the following mixed radicals into entire radicals. Verify by using a calculator to compute the numerical value of both the question and the answer. For what values of the variables in questions 2, 3, and 4 do the radicals represent real numbers?
Arranging Radicals by Size
Sometimes it will be necessary to compare and sort radicals from smallest to largest or vice versa. One method of completing this task accurately is to convert all the radicals to entire radicals. Once this is done, you only need to consider the radicands as you sort the radicals.
Read through “Example 3” on page 276 for an explanation on how this is done.
Self-Check 3
Complete “Your Turn” on page 276 of the textbook. Answer
The radical sign represents the positive root of a number. Even though (−4)2 = 16, 
. If the negative root is wanted, it must be specified as 
. If both roots are wanted, they should be specified as 
.
Skip forward to Connect if you feel you have a solid understanding of how to
- express an entire radical with a numerical radicand as a mixed radical
- express a mixed radical with a numerical radicand as an entire radical
- compare and order radical expressions in a given set
If you need a bit more practice, complete Self-Check 4.
Self-Check 4
Complete any or all of questions 3, 4, 5, 6 and 7 on pages 278 and 279 in the textbook. As you finish each part of a question, check your work against the answers given at the back of the textbook. If you are still unclear about how to answer some questions, ask your teacher about those questions and get some help.