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Question 35545: what is the 5 sqrt of 96a^12b^8?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Do you mean the FIFTH root? I have a feeling this is what you mean. If you really meant square root, then I have certainly solved the wrong problem and put you through a horrible problem for nothing. I owe you a solution to YOUR problem. Anyway, here is what I think the problem meant.
If it is a 5th root problem, then you must find perfect 5th powers that divide into this quantity. The ONLY perfect 5th power that is small enough to be used in most problems is  . It just happens (a coincidence???) that 32 is a factor of 96 and it divides into 96 exactly 3 times. Also, when you have powers involved, like  or  , you need to find a power that is DIVISIBLE by 5, which would be like  ,  ,  , etc. Now, sort this out into TWO 5th root radicals, and place all the perfect 5th powers up front in the first radical sign, and place all the leftover factors in the second radical. In this case, you will have to use and  as the perfect powers of "a" and "b" respectively. When you do a 5th root of a quantity that is raised to a power, you DIVIDE exponents. For example  and  or  .
The first radical is a perfect 5th power, so you can actually DO this one. The second radical, containing all the left-overs, will have to stay in the radical sign.
If this problem was too deep for you, or if you need additional help, check out my Lesson Plans in algebra.com for Radicals (under Square Roots) at Intermediate or College Algebra level, or see my own website under "Math in Living Color" and look for those particular topics at those levels of math.
R^2 at SCC
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