Solving Equations with Radicals

Solving equations which contain radicals involves using the squaring property of equality.  This property allows us to raise each side of an equation which contains a radical term by a power equal to the power of the index of the radical.  This will eliminate the radical and then we can solve the resulting equation using a method which we have learned earlier isolation if the equation is a first-degree equation and factoring if the equation is a quadratic (second-degree) equation.  Note:  All potential solutions from the squared equation must be checked in the original equation, since squaring could provide us with an extraneous solution.

To solve these equations involving square roots:
1) isolate the radical,
2) square both sides,
3) combine like terms,
4) determine whether the resulting equation is a first-degree (if so, use isolation to solve) or a second-
    degree (if so, use factoring to solve) and
5) check the solution for validity.

Example 1 involves a first-degree equation and Example 2 involves a second-degree equation.

Example 1.  Solve:
                                   

                                   

                                   

                                   

                                    Check:   is true and therefore a valid answer.
 

Example 2.  Solve:
                                  

                                   

                                   

                                   

                                   

                                   

                                   

                                    Therefore,  and

                       Check:  is not true and therefore  is an invalid answer.

                                    is true and therefore  is a valid answer.
 

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 15-Nov-2007