Question 307426
{{{8*sqrt(27)* sqrt(72)}}}


Break it down instead of multiplying it out.
{{{8*sqrt(9)*sqrt(3)* sqrt(36)*sqrt(2)}}}


Multiply the numbers that are OUTSIDE the square root and keep them OUTSIDE the square root.  Multiply the numbers that are INSIDE the square root and keep them INSIDE the square root, as follows:
{{{8*3*sqrt(3)*6*sqrt(2)}}}
{{{8*3*6*sqrt(3*2)}}}
{{{144 *sqrt(6)}}}


For additional explanation on square roots, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 5 for an entire chapter on Square Roots. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!! 


In addition, there is a FREE video of me teaching this topic a few years ago.  To see the video, from my Homepage, look for "Rapalje Videos in Living Color."  Choose Basic Algebra, and look for the video called "Radicals."

I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE. 


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