Solving Equations with One Radical Term
Here is a procedure that can be used to solve an equation that contains one
or more radical terms.
Procedure — To Solve a Radical Equation
Step 1 Isolate a radical term on one side of the equals sign.
Step 2 Apply the Principle of Powers.
Step 3 Solve the resulting equation. If a radical still remains, repeat
Steps 1 and 2.
Step 4 Check the solution.
Example 1
Solve for x:
| Solution Step 1 Isolate the radical term.
|
 |
= 7 |
| Add 5 to both sides. |
 |
= 12 |
| Divide both sides by 3. Step 2 Apply the Principle of Powers. |
 |
= 4 |
| Square both sides. |
 |
= 42 |
| Step 3 Solve the resulting equation.
Simplify.
Add 8 to both sides.
Divide both sides by 4.
Step 4 Check the solution. |
4x - 8
4x
x |
= 16
= 24
= 6 |
So, the solution is x = 6.
Note:
The following property can be used to
simplify radicals:
For example,
Also, recall that
 means
|