SOLUTION: Multiply: sqrt (x)^1/3 (sqrt (3x^2)^1/3 - sqrt (81x^2)^1/3)

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Question 201790: Multiply: sqrt (x)^1/3 (sqrt (3x^2)^1/3 - sqrt (81x^2)^1/3)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your formula looks like this:
if I understand it correctly.
since sqrt%28x%29 is the same as x%5E%281%2F2%29 this formula can be rewritten as follows:

since by the rules of exponents %28x%5Ea%29%5Eb is equal to x%5E%28a%2Ab%29, this formula can be rewritten as follows:
+x%5E%281%2F6%29+%2A+%28%283%2Ax%5E2%29%5E%281%2F6%29+-+%2881%2Ax%5E2%29%5E%281%2F6%29%29%29
since %28a%2Ab%29%5Ec is equal to a%5Ec%2Ab%5Ec, this formula can be rewritten as follows:

since x%5E%281%2F3%29 is a common factor, it can be factored out to get:
x%5E%281%2F6%29%2Ax%5E%281%2F3%29%2A%283%5E%281%2F6%29-81%5E%281%2F6%29%29
which simplifies to:
x%5E%281%2F2%29%2A%283%5E%281%2F6%29-81%5E%281%2F6%29%29
which i do not believe can be simplified any further, so I reduced the constants to get:
-.879146868+%2A+x%5E%281%2F2%29
to prove the answer is correct, then take any value of x and solve the original equation and then solve the reduced equation. you should get the same answer.
I did it using a value of x = 4, 12, and 27.
You can use any value you wish if you want to take the time to prove it to yourself.