Simplifying a radical with fraction and sum What are the steps to simplify
$(1+(\frac{1}{2}(x^3-\frac{1}{x^3})^2))^ \frac{1}{2}$
to
$\frac{1}{2}(x^3+\frac{1}{x^3})$ ?

Hint: Try using the identities $(a-b)^2=a^2-2ab+b^2$ and $(a+b)^2=a^2+2ab+b^2$ (which are actually the same identity).
Be careful: check whether the result holds for $x\lt0$.
I am assuming you meant
$$
\left(1+\left(\frac12\left(x^3-\frac1{x^3}\right)\right)^2\right)^{1/2}
$$
