Wetzel

Math 102

9.4 – Multiplying and Dividing Radicals

Multiplying and Dividing Radicals:

            In order to multiply and divide radicals, they must have the same index.

                                        likewise,  

Steps to Multiply & Divide Radicals:

                                    1.)  Simplify if possible.

2.)    Multiply / Divide the radicands of the radicals with the same index.

3.)    Simplify the final radical(s).

            Examples:

            1.)                       2.)                              3.) 

            4.)                                             5.) 

Rationalizing the Denominator:

            It is not considered “Simplified” to leave radicals in the denominator.

Rationalizing the Denominator means getting rid of all radicals in the denominator.

Two Methods:

I.  One Term in the Denominator:

            Steps:

            1.)  Simplify the radical.

2.)  Multiply the numerator and denominator by the radical.

3.)  Simplify the rational.

Examples:

1.)                                             2.)                                        3.) 

II.                 Two Terms in the Denominator:

            Steps:

1.)    Simplify the radical(s).

2.)    Multiply the numerator and denominator by the Conjugate of the denominator

3.)    Simplify the rational.

            Examples:

            1.)                                                              2.)