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1.4  Solving Radical Equations: Worked Examples                   

 

Example 1.  Solve           

 

Isolate the radical term:        

 

Square both sides:                    

 

Solve for x:                               

 

Check in the original equation:

 

       

 

   

 

 

 

 

Example 2.  Solve           

 

Isolate one radical term:               

 

Square both sides:                        

 

Combine like terms:                              

 

Isolate the radical term:                    

 

Square both sides:                           

 

Solve for x:                                     

 

Check in the original equation:                                             no solution

 

 

Example 3.  Solve           

 

                        

 

                        

 

                                

 

                             

 

 

 

Example 4.  Solve   

 

                          

 

                          

 

                                  

 

                            

 

 

 

 

Example 5.  Solve           

 

                          

 

                        

 

                                   

 

                                    no solution

 

 

 

Example 6.  Solve          

 

                                                

 

                        

 

                                   

 

                 

 

 

 

Example 7.  Solve           

 

                                   

 

                        

 

                                   

 

 

 

 

 

 

               

Example 8.  Solve           

 

                        

 

                                  

 

                        

  

 

  

 

 

 

             

    

 

 

Example 9.  Solve           

 

                                     

 

                        

 

                                 

 

 

 

 

Example 10.  Solve          

 

                                          

 

                        

 

                                 

 

                            

 

                           

 

 

 

 

 

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