5.03   Adding and Subtracting

           Square Roots

           from Basic Algebra: One Step at a Time © 2002

P. 413-418

Dr. Robert J. Rapalje

Seminole Community College

 

ANSWERS TO ALL EXERCISES ARE INCLUDED AT THE END OF THIS PAGE

 

To see selected solutions in Living C O L O R  click here!

 

After simplification of radicals, the next step is operations with radicals--that is, addition, subtraction, multiplication, and division of radicals.  Addition and subtraction of radicals is just like combining like terms.  Even as 3x + 4x = 7x, so it is true that .  It is also true that .  The expression  cannot be combined because and are unlike radicals.  Similarly, and cannot be  combined since  and   are unlike radicals.

EXERCISES. Combine like radicals. 

 1.                                  2.                               3.                 

     ______________                             _______________                         ______________

 

 4.                                  5.                                6.      

    _______________                            _______________                        ______________

 

 7.                                         8.                                 

     ___________________                                     _____________________

 

 9.                                        10.                      

       ___________________                                   _____________________

 

 11.                                    12.                   

       ______________________                            _______________________ 

 

13.                                                  14.         

      ______________________                             _______________________

 

15.                                                 16.         

      ______________________                             _______________________

  

17.                                                  18.        

      ______________________                             _______________________

 

19.                                            

      ___________________________                                 

 

20.                                           

         _________________________________________ 

 

21.                                     22.                      

       ______________________                            _____________________

                        

23.                                       24.                       

      ______________________                             _____________________

QUESTION:  Can  be simplified to ? 

Answer:          NO! This is a very common error!  Even as 6 - 4x cannot be combined, neither can .  It is possible to factor the common factor of 2 from  and write .  At least for now, there is no particular reason to do this.

QUESTION:  Can be combined? 

Answer:          At first glance, it appears that  and  are unlike radicals.  However, since  simplifies to , the expression can and will be combined in the next example!

EXAMPLE 1.             Combine like terms if possible for .

Solution:                                      Simplify radicals .

          Multiply 4 times 2

                Combine like radicals

 

EXAMPLE 2:             Combine like terms if possible for .

Solution:                                    Simplify the radicals.

                    

       Multiply numbers.

              Combine like radicals.

 EXAMPLE 3:             Simplify and combine like terms if possible  .

Solution:                                          Simplify radicals.

            Multiply numbers.

                        Combine like radicals.

EXERCISES.    Simplify and combine like terms if possible.

25.                       26.                          27.              

                                                 

                                                        _______________

____________                _____________     

   

28.                 29.                          30.   

 

 

 

31.                                           32.                     

                                                           

                                              

               _________________                              __________________

               _________________                              __________________        

 

33.                                           34.                             

                                                                 

              _________________                                    _____________________

             _________________                                     _____________________

             _________________                                     _____________________

 

35.                                36.          

                                        

         __________________________                     _________________________________

         __________________________                     _________________________________

         __________________________                     _________________________________

 

37.                                 38.      

 

 

 

  

39.                               40.      

 

 

  

 

41.                            42.          

  

 

 

 

EXTRA CHALLENGE

43.                                  44.      

 

 

 

 

45.                                  46.      

 

 

 

 

47.                                   48.      

  

 

 

 

49.                               50.      

 

 

 

 

ANSWERS 5.03

p. 413 - 418: 

1.; 2.; 3.; 4.; 5.; 6.; 7.;     8.; 9. ; 10.;  11.; 12.; 13.; 14.; 15.; 16.; 17.; 18.; 19.;  20.;   21.; 22.;  23.   ; 24.; 25.; 26.; 27.; 28.; 29.; 30.;  31.; 32.; 33.