Adding and Subtracting Radical Terms

The rules for the addition and subtraction of terms containing radicals are the same as for the addition and subtraction of  “like terms.”  You may add or subtract the coefficients of terms which contain the same radical … same exact radical, with same exact radicand.  Remember that if the term contains other variable factors, those factors must also be exactly alike.  For example,  and  are like terms and may be combined by combining their coefficients … .  Likewise,  and  are like terms and  and  are not like terms and may not be combined.  Likewise,  and  are not like terms and may not be combined.

When adding or subtracting radicals, you must examine the radicals and make sure that they are fully simplified before adding the coefficients.  Once the radicals are simplified, examine all terms to determine “like terms” before combining.  For example:
Notice that once you have simplified the radicals, the “rational” part of the radicand that comes out from underneath the radical will multiply the existing coefficient to form a new coefficient.

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 15-Nov-2007