5.03  Adding and Subtracting Square Roots

Basic Algebra: One Step at a Time.  Page 413-418:   #28, 29, 37, 38, 41.

Dr. Robert J. Rapalje

Seminole Community College

Sanford, FL  32773

To see Section 5.03, with detailed explanations, examples, exercises, and answers, click here!

p. 416-417:

   28.                  

           Make two separate radicals for each of the radicals above:

           Find a perfect square factor in  each of the above, place it in the (first) RED radical.

            Place the other factor that is “left-over” in the (second) BLUE radical.

            Take square roots of the perfect squares:

            Since these are NOT  LIKE radicals, you CANNOT combine them. 

This is the final answer:  

           Calculator check:     =  18.251

                                                      =  18.251

   29.                  

           Make two separate radicals for each of the radicals above:

           Find a perfect square factor in  each of the above, place it in the (first) RED radical.

            Place the other factor that is “left-over” in the (second) BLUE radical.

            Take square roots of the perfect squares:

            Since these are LIKE radicals, you can combine them:

           Calculator check:   =  15.556

                                                              =  15.556

37.                     

    Make two separate radicals for each of the radicals above:

    Find a perfect square factor in  each of the above, place it in the (first) RED radical.

    Place the other factor that is “left-over” in the (second) BLUE radical.

    Take square roots of the perfect squares:

    Multiply the numbers together:

    Notice that the first two terms are both  terms?  Combine these, but leave the other.

    FINAL ANSWER:         

    Calculator check:       =  −24.359

                                                     =  −24.359

   38.                 

    Make two separate radicals for each of the radicals above:

    Find a perfect square factor in  each of the above, place it in the (first) RED radical.

    Place the other factor that is “left-over” in the (second) BLUE radical.

    Take square roots of the perfect squares:

     Multiply the numbers together:

      Notice that they are all  terms?  Combine all like terms: (24– 40 + 21 = 5)

      FINAL ANSWER:       

      Calculator check:       =  7.071

                                                                 =  7.071

   41.                  

           Make two separate radicals for each of the radicals above:

           Find a perfect square factor in  each of the above, place it in the (first) RED radical.

            Place the other factor that is “left-over” in the (second) BLUE radical.

            Take square roots of the perfect squares:

            Multiply the numbers together:

            Notice that they are all  terms?  Combine all like terms: (15+ 14 – 40 = -11)

   Calculator check:       =  −29.103

                                                                                      =  −29.103

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