SOLUTION: Simplify {{{root(3,a)(root(3,3a^2)+root(3,81a^2))}}}

Algebra ->  Radicals -> SOLUTION: Simplify {{{root(3,a)(root(3,3a^2)+root(3,81a^2))}}}      Log On


   

Question 126524: Simplify

root%283%2Ca%29%28root%283%2C3a%5E2%29%2Broot%283%2C81a%5E2%29%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2Ca%29%28root%283%2C3a%5E2%29%2Broot%283%2C81a%5E2%29%29 Start with the given expression



root%283%2Ca%29%2Aroot%283%2C3a%5E2%29%2Broot%283%2Ca%29%2Aroot%283%2C81a%5E2%29 Distribute


root%283%2C%28a%29%2A%283a%5E2%29%29%2Broot%283%2C%28a%29%2A%2881a%5E2%29%29 Combine the roots


root%283%2C3a%5E3%29%2Broot%283%2C81a%5E3%29 Multiply


a%2Aroot%283%2C3%29%2B3a%2Aroot%283%2C3%29 Simplify root%283%2C3a%5E3%29 to get a%2Aroot%283%2C3%29. Simplify root%283%2C81a%5E3%29 to get 3a%2Aroot%283%2C3%29.


root%283%2C3%29%28a%2B3a%29 Factor out the GCF root%283%2C3%29


root%283%2C3%29%284a%29 Combine like terms


4a%2Aroot%283%2C3%29 Rearrange the terms




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Answer:


So root%283%2Ca%29%28root%283%2C3a%5E2%29%2Broot%283%2C81a%5E2%29%29 simplifies to 4a%2Aroot%283%2C3%29



In other words, root%283%2Ca%29%28root%283%2C3a%5E2%29%2Broot%283%2C81a%5E2%29%29=4a%2Aroot%283%2C3%29