Solving Radical Equations
To solve an equation with a square root, we square both sides. To solve
an equation with a cube root, we cube both sides. If the index of the
radical is 4, we raise each side to the fourth power, and so on.
Example 1
Solve for x:
| Solution |
 |
= 5 |
| Step 1 Isolate the radical term.
Subtract 2 from both sides.
Step 2 Apply the Principle of Powers.
|
 |
= 3 |
| Cube both sides.
|
 |
= 33 |
| Step 3 Solve the resulting equation.
Simplify.
Add 5 to both sides.
Divide both sides by 2. Step 4 Check the solution. |
2x - 5
2x
x |
= 27
= 32
= 16 |
So, the solution is x = 16.
Example 2
Solve for x:
| Solution |
 |
= 8 |
| Step 1 Isolate the radical term.
Subtract 5 from both sides.
Step 2 Apply the Principle of Powers. |
 |
= 3 |
| Raise both sides to the fourth power.
|
 |
= 34 |
| Step 3 Solve the resulting equation. Simplify.
Subtract 9 from both sides.
Divide both sides by 6. Step 4 Check the solution.
The check is in the side note.
So, the solution is x = 12. |
6x + 9
6x
x |
= 81
= 72
= 12 |
|