SOLUTION: please help sqrt75t^3+8sqrt108t^3

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Question 67496: please help
sqrt75t^3+8sqrt108t^3

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
please help 

+sqrt%2875t%5E3%29%2B8sqrt%28108t%5E3%29+

Break everything down into prime factors with
no exponents showing:


+sqrt%283%2A5%2A5%2At%2At%2At%29%2B8sqrt%282%2A2%2A3%2A3%2A3%2At%2At%2At%29+

Since it's a square root, pair up groups of two
(pairs) of like factors:




The pair of 5's and the pair of t's under the first radical
come out front as a single 5 and a single t, the 3 and the
t that did not pair up stay under the radical:


+5%2At%2Asqrt%283%2At%29%2B8sqrt%28%282%2A2%29%2A%283%2A3%29%2A3%2A%28t%2At%29%2At%29+

The pair of 2's, the pair of 3's, and the pair of t's under
the second radical come out front as a single 2, a single 3,
and a single t, the 3 and the t that did not pair up stay 
under the radical:

      +5%2At%2Asqrt%283%2At%29%2B8%2A2%2A3%2At%2Asqrt%283%2At%29+

      +5t%2Asqrt%283t%29%2B48t%2Asqrt%283t%29+

Factor out t%2Asqrt%283t%29

      +t%2Asqrt%283t%29%285+%2B+48%29

      +t%2Asqrt%283t%29%2853%29

      +53t%2Asqrt%283t%29

Edwin