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Question 240633: Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
sqrt of 20a^2b
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 
You need to separate this square root into TWO square roots. Place all the PERFECT SQUARE factors in the first square root and the leftover factors in the second square root. In this case, the perfect squares are 4 and a^2. The leftover factors are 5 and b. It looks like this:
Now, you can DO the square root of the first radical, since it IS a perfect square. However, the SECOND square root is NOT a perfect square, you CAN'T do it, so LEAVE IT ALONE (in the radical sign!):
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
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