SOLUTION: How do I simplify {{{ root(3,54c^4) }}}

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Question 286501: How do I simplify +root%283%2C54c%5E4%29+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+root%283%2C54c%5E4%29+ Start with the given expression.


+root%283%2C2%2A27%2Ac%5E3%2Ac%29+ Factor 54 into 2*27 (note how 27 is a perfect cube) and factor c%5E4 into c%5E3%2Ac


+root%283%2C2%29%2Aroot%283%2C27%29%2Aroot%283%2Cc%5E3%29%2Aroot%283%2Cc%29+ Break up the root.


+root%283%2C2%29%2A3%2Ac%2Aroot%283%2Cc%29+ Take the cube root of 27 to get 3. Take the cube root of c%5E3 to get c.


+3c%2Aroot%283%2C2c%29+ Rearrange the terms and combine the roots.


So +root%283%2C54c%5E4%29+=+3c%2Aroot%283%2C2c%29+