TUTORIALS:

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.


= 3^{3} 
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.


= 3^{4} 
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 
