Question 241015
The first step in simplifying a square root is to SORT it into TWO square roots where the first square root contains only perfect squares, and the second square root has all the "left-over" factors.  Remember also that if you have a variable raised to a power, if the power is EVEN, like x^4 or y^8, then this IS a perfect square, and to take the square root, you take HALF of the exponent.  


Okay?  Here we go:
{{{sqrt(18x^4y^8)}}}
{{{sqrt(____)*sqrt(____) }}}
{{{sqrt(9x^4y^8)*sqrt(2) }}}


Now, take the square root of the first one, since it IS a perfect square.  Remember, to take HALF of the exponents!  However, the second square root is NOT a perfect square, so just leave it like it is!

{{{3x^2y^4*sqrt(2)}}}


I have a LOT of resources on my own website on the topic of SQUARE ROOTS.  To find my website, do a "BING" or a "GOOGLE" search for my last name "Rapalje".  Near the top of the search list, you should see "Rapalje Homepage."  Click on this, and look near the top of my homepage for the link "Basic, Intermediate and College Algebra: One Step at a Time."  Choose "Basic Algebra", and look in "Chapter 5" for "Section 5.01, Square Roots."  This is my own explanation especially written for students who have trouble understanding math.  I wrote this to students, NOT mathematicians, and I think you will find it easier to understand than your own traditional textbooks!!  In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR.  


In addition, I have a video of me teaching this topic in the classroom a few years ago.  To see this FREE video, from my Homepage, look for "Rapalje Videos in Living Color".  Select "Basic Algebra", and look for "Radicals (Square Roots)".  


If you like my website, please recommend it to family and friends who have trouble understanding math!!  It's ALL FREE!!!


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