SOLUTION: IN response to the answer give for Question 201790 This problem is actually cube root form written as sqrt (x)^1/3. The ^1/3 means that each square root has a cube root. If you

Algebra ->  Radicals -> SOLUTION: IN response to the answer give for Question 201790 This problem is actually cube root form written as sqrt (x)^1/3. The ^1/3 means that each square root has a cube root. If you      Log On


   

Question 201810: IN response to the answer give for Question 201790
This problem is actually cube root form written as sqrt (x)^1/3. The ^1/3 means that each square root has a cube root. If you could please help me again with this problem.
Cube root sqrt (x) (cube root sqrt (3x^2) - cube root sqrt (81x^2))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
note: you can say "root(3,x)" to mean root%283%2Cx%29. Or you can simply say "the cube root of 2" to mean root%283%2C2%29



root%283%2Cx%29%2A%28root%283%2C3x%5E2%29-root%283%2C81x%5E2%29%29 Start with the given expression.


root%283%2Cx%29%2Aroot%283%2C3x%5E2%29-root%283%2Cx%29%2Aroot%283%2C81x%5E2%29 Distribute


root%283%2Cx%2A3x%5E2%29-root%283%2Cx%2A81x%5E2%29 Combine the roots using the identity root%28n%2Cx%29%2Aroot%28n%2Cy%29=root%28n%2Cx%2Ay%29


root%283%2C3x%5E3%29-root%283%2C81x%5E3%29 Multiply


root%283%2C3x%5E3%29-root%283%2C27%2A3x%5E3%29 Factor 81 into 27*3. Note: one factor must be a perfect cube.


Break up the roots.


root%283%2C3%29%2Aroot%283%2Cx%5E3%29-3%2Aroot%283%2C3%29%2Aroot%283%2Cx%5E3%29 Evaluate the cube root of 27 to get 3.


root%283%2C3%29%2Ax-3%2Aroot%283%2C3%29%2Ax Evaluate the cube root of x%5E3 to get "x".


x%2Aroot%283%2C3%29-3x%2Aroot%283%2C3%29 Rearrange the terms and multiply


%28x-3x%29%2Aroot%283%2C3%29 Factor out the GCF root%283%2C3%29


-2x%2Aroot%283%2C3%29 Combine like terms.



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Answer:


So root%283%2Cx%29%2A%28root%283%2C3x%5E2%29-root%283%2C81x%5E2%29%29=-2x%2Aroot%283%2C3%29