Lesson 7

Lesson 7 Summary

 

Radical equations are used to solve problems in many situations. The key to success lies in translating the word problems into mathematical symbols. Some problems give you both the equation and the values needed to solve the equation. You can then state any restrictions on the variables and proceed to solve the equation. There are, however, problems where you are given information about a situation and you need to combine different formulas to develop an equation in order to solve the problem.

 

When you solve a radical equation, you will use inverse operations to first isolate the radical and then eliminate the radical sign. Before you solve the equation, you need to state any restrictions on any variables provided. This ensures that the radicand of a square root is not negative or that the answer is reasonable. For example, if you are solving a problem about the distance from a planet to the Sun, you need to state that the answer cannot be negative because distances are not negative.

 

In the process of solving radical equations, you often need to square a radical to remove the radical sign. This may, however, introduce an invalid solution called an extraneous root; so you need to verify each solution by substituting it back into the original equation.

 

You have used radical expressions and equations to help solve a variety of problems. Now refer to the Module 5 Summary for an overview of concepts you investigated in this module.