SOLUTION: Simplify {{{(root(5,9)-root(5,81))/(root(5,3))}}}

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Question 148158: Simplify %28root%285%2C9%29-root%285%2C81%29%29%2F%28root%285%2C3%29%29
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%28root%285%2C9%29-root%285%2C81%29%29%2F%28root%285%2C3%29%29 Start with the given expression.


%28root%285%2C9%29-root%285%2C9%2A9%29%29%2F%28root%285%2C3%29%29 Factor 81 into 9*9


%28root%285%2C9%29-root%285%2C9%29%2Aroot%285%2C9%29%29%2F%28root%285%2C3%29%29 Break up the root.


%28root%285%2C9%29%281-root%285%2C9%29%29%29%2F%28root%285%2C3%29%29 Factor out the GCF root%285%2C9%29


%28root%285%2C3%2A3%29%281-root%285%2C9%29%29%29%2F%28root%285%2C3%29%29 Factor 9 into 3*3


%28root%285%2C3%29%2Aroot%285%2C3%29%281-root%285%2C9%29%29%29%2F%28root%285%2C3%29%29 Break up the root.


%28highlight%28root%285%2C3%29%29%2Aroot%285%2C3%29%281-root%285%2C9%29%29%29%2F%28highlight%28root%285%2C3%29%29%29 Highlight the common terms.


%28cross%28root%285%2C3%29%29%2Aroot%285%2C3%29%281-root%285%2C9%29%29%29%2F%28cross%28root%285%2C3%29%29%29 Cancel out the common terms.


root%285%2C3%29%281-root%285%2C9%29%29 Simplify


root%285%2C3%29%2A1-root%285%2C3%29%2Aroot%285%2C9%29%29 Distribute


root%285%2C3%29-root%285%2C27%29 Combine the roots and multiply


So %28root%285%2C9%29-root%285%2C81%29%29%2F%28root%285%2C3%29%29 simplifies to root%285%2C3%29-root%285%2C27%29

In other words, %28root%285%2C9%29-root%285%2C81%29%29%2F%28root%285%2C3%29%29=root%285%2C3%29-root%285%2C27%29

Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
The 5th root of 3 is a common denominator.
Divide each term by the common denominator to get:
3^(!/5) - 27^(1/5)
======================
Cheers,
Stan H.