Question 213542
Do you mean {{{6*sqrt(3) +8*sqrt(3) -16*sqrt(3) }}}"?


If so, then it's like combining like terms.  

     You know that 6x +8x -16x = -2x

     You know that 6y+8y-16y =-2y


In this case, instead of combining "like terms," you are combining "like radicals."  Since these are "like radicals", you can combine them like this:


{{{6*sqrt(3) +8*sqrt(3) -16*sqrt(3) =-2*sqrt(3)}}}


For additional information on combining square roots, see my own website.  You can do a "Bing" search for my last name "Rapalje".  At the top of the search list, look for "Rapalje Homepage".  Near the top of my Homepage, look for the link "Basic, Intermediate and College Algebra: One Step at a Time."  Choose "Basic Algebra" and look for Chapter 5 Radicals.  This particular question is explained in Section 5.02 "Adding and Subtracting Radicals."


In addition to the written explanations, I now have free videos on a variety of topics, including "Square Roots".  To find this page, look on my Homepage for "Rapalje Videos," and look in "Basic Algebra" for the video on "Radicals".


R^2


Dr. Robert J. Rapalje, Retired
Seminole Community College
Altamonte Springs Campus
Florida