Lesson 4
Completion requirements
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1. Lesson 4
1.6. Explore 2
Module 5: Radicals
Try This 2
Open Relations and Functions: Radical Equations. Work through the introduction, tutorials, and example questions. Think about the following questions as you do:
- How do the steps used to solve the radical equations (finding the roots) in the applet compare to the steps you used in Try This 1?
- What are extraneous roots and how are they determined?
- What techniques can help you solve radical equations containing two radicals?
Example 1: Equations that Include a Radical Term
Take a look at another example of the solution to an equation that includes a radical term on page 296 in the textbook.
- Notice in part a. of the solution that the restrictions for variable x are described. The radicand must be greater than or equal to zero to take a square root. Remember that when taking a square root, the index is even since it is 2, and roots cannot be taken of negative numbers when the index is even.
- Another restriction that may exist in future problems is that the denominators cannot equal zero.
Example 2: Extraneous Solutions to Radical Equations
Khan Academy CC BY-NC-SA 3.0
Watch “Extraneous Solutions to Radical Equations.” As you do, think about the following:
- The quadratic formula is used to help find the roots in this example. Could you find the roots without using the quadratic formula?
- An explanation of why extraneous solutions occur is given in this video. How does this explanation compare to the explanation in Try This 2?
Self-Check 1
What restrictions are there on the values of the variables in each of the following equations if the equations involve real numbers? Solve and check each of the equations to make sure there are no extraneous roots.
