Apple's NSDecimalNumber can be useful in cases where you need to maintain more precision that a double would provide. However, it's a little on the sparse side to say the least.

Here's a category that I've come up with to implement square and cube roots methods for NSDecimalNumber using Newton's method. It is loosely based on some code from Matt Gallagher. Many thanks to Matt for the original version.

The most obvious change that I've made is to convert the code into a category and to extend it to also support cube root calculation. There's a couple of other bonus methods thrown in for free (equivalence tests, sign and absolute value).

On top of that I tweaked the algorithm to iterate until the given level of precision is reached, rather than just using a set number of iterations. As a final touch the return value is tested for equivalence with it's "intValue" and the rounded intValue is returned if the test passes.

Note that I can't vouch for the performance of this code. It's fine for most uses, but don't use it to simulate fluid dynamics.