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.