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:
The following procedure may be used to solve an equation that contains a
variable under a square root symbol.
Procedure â€” To Solve an Equation That Contains a Variable
Under a Square Root Symbol
Step 1 Isolate the squareroot 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:
Solution


Step 1 Isolate the squareroot radical
on one side of the equation.
Add 3 to both sides of the equation.


Step 2 Square both sides of the equation.
Simplify.


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. 



So, x = 50 is the solution of the radical equation.
Example 2
Solve:
Solution


Step 1 Isolate the squareroot radical
on one side of the equation.
Subtract 4 from both sides of the equation.


Step 2 Square both sides of the equation.
Simplify.


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. 



So, x = 27 is the solution of the radical equation.
