Wetzel

Math 102

9.3 – Simplifying, Adding, & Subtracting Radicals

Simplifying:

            1.)  Identify n, the index.

2.)  For Constants:  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.

3.)  For Variables:  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 the following.

            1.)                            2.)                          3.) 

Adding / Subtracting Radicals:

            Add and subtract radicals as if they were variables!

In order to add and subtract variables, you must have like terms.  In order to add and subtract radicals, you must have like radicals.

Like radicals are radicals that have the same index and radicand.

            Steps To Add & Subtract Radicals:

1.)    Simplify all radicals.

2.)    Combine like radicals.

Review Variables:   = ______________________

Now Radicals:    = ______________________

Examples:

1.)                   2.) 

3.)