SOLUTION: Simplify {{{(root(5,4)-root(5,2))(root(5,125)+root(5,8))}}}

Algebra ->  Radicals -> SOLUTION: Simplify {{{(root(5,4)-root(5,2))(root(5,125)+root(5,8))}}}      Log On


   

Question 126405: Simplify

%28root%285%2C4%29-root%285%2C2%29%29%28root%285%2C125%29%2Broot%285%2C8%29%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28root%285%2C4%29-root%285%2C2%29%29%28root%285%2C125%29%2Broot%285%2C8%29%29 Start with the given expression


Now let's FOIL the expression



Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:%28root%285%2C4%29%29%2A%28root%285%2C125%29%29=root%285%2C4%2A125%29=root%285%2C500%29






Multiply the Outer terms:%28root%285%2C4%29%29%2A%28root%285%2C8%29%29=root%285%2C4%2A8%29=root%285%2C32%29


Now simplify root%285%2C32%29 to get 2. In other words, root%285%2C32%29=2



Multiply the Inner terms:%28-root%285%2C2%29%29%2A%28root%285%2C125%29%29=-root%285%2C2%2A125%29=-root%285%2C250%29



Multiply the Last terms:%28-root%285%2C2%29%29%2A%28root%285%2C8%29%29=-root%285%2C2%2A8%29=-root%285%2C16%29


root%285%2C500%29%2B2-root%285%2C250%29-root%285%2C16%29 Now collect every term to make a single expression



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Answer:
So %28root%285%2C4%29-root%285%2C2%29%29%28root%285%2C125%29%2Broot%285%2C8%29%29 foils and simplifies to root%285%2C500%29%2B2-root%285%2C250%29-root%285%2C16%29

In other words,