Wetzel

Math 102

9.1 – Square Roots; Radical Notation

Review:

·        Polynomials

·        Terms

·        Factors

·        Exponents

Radicals:

                        Square Roots, Cube Roots, ….n-th Roots

                                                     where n is called the index

            Perfect Squares:   1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 625

            Perfect Cubes:    1, 8, 27, 64, 125, 1000

            To Simplify Radicals of a Constant:

                        1.)  Identify n, the index.

                        2.)  If the radicand is a perfect n-th root, find the root.

                              If the radicand is NOT a perfect n-th root, determine if the radicand  has any factors that are perfect n-th roots.  Work the perfect roots

                            and leave what’s left over in the radical.

            Examples:  Simplify.

1.)                                                2.)                                                    3.)                                   

 

 

 

 

 

 

            4.)                                             5.)                                                         6.) 

            **If the index is even and the radicand is negative, there is no real solution!      

            Root of a variable:

            To Simplify Radicals of a Variable:

                        1.)  Determine how many times n will divide into the exponent of the variable without going over.  This number will be the variable’s

                         new exponent outside the radical.  Any remainder will be the variable’s exponent still inside the radical.

            Examples:  Simplify

            1.)                                                                                   2.)                

                 3.)                                                                                 4.)