SOLUTION: How do you solve this problem? I think I'm carrying the cubed root out wrong or something. (x+3)^3=-16

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Question 820127: How do you solve this problem?
I think I'm carrying the cubed root out wrong or something.
(x+3)^3=-16
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3%29%5E3=-16
You are right in thinking to use a cube root:
root%283%2C+%28x%2B3%29%5E3%29=root%283%2C+-16%29
Simplifying...
x%2B3=root%283%2C+-8%2A2%29
x%2B3=root%283%2C+-8%29%2Aroot%283%2C+2%29
x%2B3=%28-2%29%2Aroot%283%2C+2%29
Adding -3:
x=-3%2B%28-2%29%2Aroot%283%2C+2%29
This is an exact expression for the solution. (Note: If we had factored out 8 earlier instead of -8 we would have x=-3%2B2%2Aroot%283%2C+-2%29 which is probably just as good as the earlier expression. I prefer the "-" outside the radical so I like the other solution better.)

P.S. If you need a decimal approximation and you don't know how to find cube roots on your calculator, then raise the 2 to the 1/3 power. If your calculator has buttons for parentheses you could enter:
2^(1/3)
If there are no parentheses buttons then use a decimal for 1/3. (Since 1/3 as a decimal has an infinitely repeated digit, 3. Use as many 3's as you can:
2^0.3333333...