Learning Objectives:

__Math Tutoring on Solving Radical Equations__

Here are the steps we will follow to solve equations having one **r****adical: **

1. We will **isolate** the **radical **on one side of the equation.

2. Then we are going to **raise** both sides of the equation to the **power **of the** index.**

** **3. We will now **solve** and **check** our solutions.

The reason it is so important to check our solutions this time as some solutions may not work and these are called **extraneous solutions**. **Squaring **and** square rooting** are opposite operations so these two **undo** each other leaving us with just** x** which obviously makes solving the equation much easier. The same thing is true for any index. Now we see how to solve **radical equations **with** two radicals.** So here are the steps that we will follow:

**1.** We are going to put **one radical** on each side of the **equal sign.**

**2.** Then we will raise both sides of the equation to the **power **of the** index** just like last time.

**3.** However, now if **one radical** remain, we are going to have to **isolate** the remaining radical and raise both sides to the power of the index again, solve again and then check answers.

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**Hook Questions:**

*1. What is a radical equation? *

*2. How do you solve an equation with two radicals? *

*3. What is an extraneous solution to a radical equation?*

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