Solving an Equation That Contains a Square Root
An equation with a variable in a radicand is called a radical equation.
Here are three examples:
![](./articles_imgs/1094/solvin92.gif)
The following procedure may be used to solve an equation that contains a
variable under a square root symbol.
Procedure — To Solve an Equation That Contains a Variable
Under a Square Root Symbol
Step 1 Isolate the square-root radical on one side of the equation.
Step 2 Square both sides of the equation.
Step 3 Solve for the variable.
Step 4 Check the answer.
Example 1
Solve:
![](./articles_imgs/1094/solvin93.gif)
Solution
|
![](./articles_imgs/1094/solvin93.gif) |
Step 1 Isolate the square-root radical
on one side of the equation.
Add 3 to both sides of the equation.
|
![](./articles_imgs/1094/solvin94.gif) |
Step 2 Square both sides of the equation.
Simplify.
|
![](./articles_imgs/1094/solvin95.gif) |
Step 3 Solve for the variable.
Divide both sides by 2.
|
x = 5 |
Step 4 Check the answer.
To check, substitute 50 for x in the original
equation and simplify. |
![](./articles_imgs/1094/solvin96.gif) |
|
![](./articles_imgs/1094/solvin97.gif) |
So, x = 50 is the solution of the radical equation.
Example 2
Solve:
![](./articles_imgs/1094/solvin98.gif)
Solution
|
![](./articles_imgs/1094/solvin99.gif) |
Step 1 Isolate the square-root radical
on one side of the equation.
Subtract 4 from both sides of the equation.
|
![](./articles_imgs/1094/solvin1.gif) |
Step 2 Square both sides of the equation.
Simplify.
|
![](./articles_imgs/1094/solvin2.gif) |
Step 3 Solve for the variable.
Add 5 to both sides of the equation.
Divide both sides by 2.
|
2x = 54 x = 27 |
Step 4 Check the answer.
To check, substitute 27 for x in the original
equation and simplify. |
![](./articles_imgs/1094/solvin3.gif) |
|
![](./articles_imgs/1094/solvin4.gif) |
So, x = 27 is the solution of the radical equation.
|