SOLUTION: Hello, I have a problem with this radical! Please help, I don't understan it at all so I don't have any work to show. Sorry.... find x if (Sqrt x sqrt x)^3=9 p.s. the second

Algebra ->  Radicals -> SOLUTION: Hello, I have a problem with this radical! Please help, I don't understan it at all so I don't have any work to show. Sorry.... find x if (Sqrt x sqrt x)^3=9 p.s. the second      Log On


   

Question 186067This question is from textbook
: Hello, I have a problem with this radical! Please help, I don't understan it at all so I don't have any work to show. Sorry....
find x if (Sqrt x sqrt x)^3=9
p.s. the second radical is inside the first and the entire thing is cubed This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find x if (Sqrt x sqrt x)^3=9
Assume you mean
%28sqrt%28x%2Asqrt%28x%29%29%29%5E3 = 9
:
Find the cube root of both sides
sqrt%28x%2Asqrt%28x%29%29 = 9%5E%281%2F3%29
Write it using exponents on the inside radical
sqrt%28x%2Ax%5E%281%2F2%29%29 = 9%5E%281%2F3%29
:
sqrt%28x%5E%283%2F2%29%29 = 9%5E%281%2F3%29
:
%28x%5E%283%2F2%29%29%5E%281%2F2%29 = 9%5E%281%2F3%29
:
x%5E%283%2F4%29 = 9%5E%281%2F3%29
Cube both sides
%28x%5E%283%2F4%29%29%5E3 = 9
:
x%5E%289%2F4%29 = 9
:
x = 9%5E%284%2F9%29
x ~ 2.655
:
:
Check solution on a calc: enter %28sqrt%282.655%2Asqrt%282.655%29%29%29%5E3 = 8.997 ~ 9