Thanks Manatee - just spent a happy while prodding about with that. As you say, Excel throws its apron over its head and runs from the room screaming, but Bing just works it out. But that isn't very satisfactory, so I've just "proved" to myself that it's right by doing the sum longhand, which was tedious but vaguely satisfying.
The deeper questions that occur to you with this cube root thing, such as "why, what's extra special about 42" or "why is 1 so intuitive and easy" or "where does any other number lie on that line between easy and bizarrely hard to solve, and why", or if there is indeed a "why" to be found here at all is fascinating though, as with much maths.
It's coincidental - the same mathematician was describing to me recently how to work out cube roots from first principles.
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