SOLUTION: please help me with this problem. x^3/2=10.42

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Question 113363: please help me with this problem.
x^3/2=10.42
Found 3 solutions by checkley71, solver91311, VVNRAMESH:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
x^3/2=125
x^3/2=125
x^3/2=5^3
sqrtx^3=5^3
sqrtx=5 now square both sides.
x=5^2
x=25 answer.
proof
25^3/2=125
sqrt25^3=125
sqrt(25*25)(5*5)=125
25*5=125
125=125


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I presume you want to solve for x.

x%5E%283%2F2%29=125. This is equivalent to %28sqrt%28x%29%29%5E3=125. In general, x%5E%28a%2Fb%29=%28root%28b%2Cx%29%29%5Ea

So the first thing to do is to take the cube root of both sides of the equation:

root%283%2Cx%5E%283%2F2%29%29=root%283%2C125%29
sqrt%28x%29=5 (because 5 X 5 X 5 = 125, and because x%5E%281%2F2%29=sqrt%28x%29)

Then you need to square both sides:

%28sqrt%28x%29%29%5E2=5%5E2

x=25. Done.

By the way, the steps I used don't have to be done in that order. We could have squared 125 to get 15625 and then taken the cube root of 15625 to get 25. I did it the way I did because the numbers stayed smaller so the arithmetic was easier.

Hope this helps,
John

Answer by VVNRAMESH(1) About Me  (Show Source):