Lesson 6

Lesson 6 Summary

 

When you are solving radical equations, the first consideration is to determine whether there are restrictions on the variable. Recall from previous lessons that you always determine restrictions on the original equation. Not all numbers can be used for variables in a radical equation. If the radicand is in the denominator, the value of the radicand cannot allow the denominator to equal zero. Also, if the index is an even number, the radicand must not have a negative value.

 

The first step in solving a radical equation is to isolate the radical. Once the radical is isolated, you can eliminate the radical sign. To do this, you square both sides of the equation (i.e., if the radical is a square root) or cube both sides of the equation (i.e., if the radical is a cube root). Once you have eliminated the radical sign, you solve for the variable using algebra. This may involve using inverse (or opposite) operations, or it may involve factoring trinomials.

 

Sometimes in the process of solving a radical equation, you can find a root (also called a solution) that is not a solution to the original equation. This is known as an extraneous root. As you discovered in the Explore section, the process of squaring both sides of an equation changes the possible solution set from those values that lie on a portion of a parabola to those values that lie on an entire parabola. The only way to be sure which roots are solutions is to substitute the roots one at a time into the original equation. If both the left side and right side of the equation are equal, the root is a solution to the equation. If both sides are not equal when the root is substituted in, the root is extraneous (not a solution).

 

In the next lesson you will model situations using radical equations. You will use the ability to solve the equations that you developed in this lesson to answer questions about that situation.