Solving Equations Containing Radical Expressions

To solve an equation with a radical expression, you need to isolate the variable on one side of the equation. We will solve an equation together. Factor out the GCF Next

Multiply by conjugate.

Don’t forget to check your work.

Let’s solve another example together. Square each side. Combine like terms. Divide by 6. Square each side again. Next

Check: n=2 Since the root of x=2 does not check, it is called an extraneous solution.

Check #2: n = 27 The solution is n=27.

We will do this last example together. Add 10 to each side. Divide each side by 5. Cube each side.

Check: y=3 Substitute into the original equation.

Now, you do some on your own.

A radical equation can also be solved graphically. Here is an example to do using your graphing calculator.

The first step is to set each side of the equation equal to y so the equation looks like this: Now graph the equations on your calculator.

Here is what the graphs should look like.

Looking at the graph, the x-coordinate is the solution. Therefore the answer is 3. Try this one on your own. The answer is x = 1.25