SOLUTION: I am having trouble with a type of cubed root problem and cannot find it im my book. It is written as: the cubed root of x the square root of x =9. Now, the radicand for square roo

Question 525334: I am having trouble with a type of cubed root problem and cannot find it im my book. It is written as: the cubed root of x the square root of x =9. Now, the radicand for square root of x is ALSO inside the radicand for the cubed root of x. It looks like this: index of 3, radicand with x inside, as well as smaller radicand with x inside, equals 9. I can find no information on how to solve these "double roots"
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It is written as: the cubed root of x the square root of x =9. Now, the radicand for square root of x is ALSO inside the radicand for the cubed root of x. It looks like this: index of 3, radicand with x inside, as well as smaller radicand with x inside, equals 9. I can find no information on how to solve these "double roots"
-----------------------
Equation:
cbrt[x*sqrt(x)] = 9
----
Raise both sides to the 3 power to get:
x*sqrt(x) = 729
----
x^(3/2) = 728
-----
Raise both sides to the 2/3 power to get:
x = 729^(2/3)
---
x = 9^2
x = 81
-----------------
Cheers,
Stan H.
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