Question 820127
{{{(x+3)^3=-16}}}
You are right in thinking to use a cube root:
{{{root(3, (x+3)^3)=root(3, -16)}}}
Simplifying...
{{{x+3=root(3, -8*2)}}}
{{{x+3=root(3, -8)*root(3, 2)}}}
{{{x+3=(-2)*root(3, 2)}}}
Adding -3:
{{{x=-3+(-2)*root(3, 2)}}}
This is an exact expression for the solution. (Note: If we had factored out 8 earlier instead of -8 we would have {{{x=-3+2*root(3, -2)}}} which is probably just as good as the earlier expression. I prefer the "-" outside the radical so I like the other solution better.)<br>
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...