An equation in which the unknown appears in a radicand is called a radical equation.
For instance:     and     are radical equations.

            To solve a radical equation, begin by isolating the most complicated radical expression on one side of the equation, and then eliminate the radical by raising both sides of the equation to a power equal to the index of the radical. You may have to repeat this technique in order to eliminate all radical. When the equation is radical-free, simplify and solve it. Since extraneous roots may be introduced when both sides of an equation are raised to even powers, all roots must be checked by substitution in the original equation whenever a radical with an even index is involved.

Example:
            Solve
Solution:
            To isolate the radical, we add to both sides of the equation
                                   
            Now we raise both sides to the power and obtain
                                        or  
            It follows that. Since we did not raise both sides of the equation to an even power, it is not necessary to check our solution, but its good practice to do so anyway. Substituting in the left side of the original equation, w obtain
                       
            Hence, the solutionis correct.

Example:
            Solve
Solution:
            We add to both sides of the equation to isolate  on the left side. Thus
                                     
            Now we square both sides of the equation to obtain     
                                   
                                   
            The equation still contains a radical, so we simplify and isolate this radical
                                   
                                   
            Again, we square both sides, so we get
                                   
                                   
                                   
                                   
                                     or         
            For Check:
                        ; hence,  is a solution.
            For Check:
                       
            Therefore, is an extraneous root that was introduced by squaring both sides of the equation. The only solution