Before you carry that sofa up the stairs, you might want to take out
some paper and a pencil (or, these days, a calculator) and figure out
if you're going to be able to get it around the right-angled corner on
the second floor. Here's how to tell.

First, trudge on up to the second floor. Now, skip lightly down the
stairs[1], get your tape measure, and return to the mezzanine.
Next, measure the width of the corridor on both sides of the corner; call
these widths **x** and **y**. For example,

---------------------+
2 |
-------------+ |
| |
| |
| 4 |
| |

Now, evaluate the

expression
(*x*^{2/3} + *y*^{2/3})^{3/2}
This value is the length of the longest rigid object that you can
get around the corner[2]. In the example, that would be about
8 and one third.

It may be helpful to remember that

*n*^{ab} = *n*^{ab}
thus,

*n*^{2/3} is the

cube root of the

square of

*n*
(or the square of the cube root of

*n*, if you prefer).

But remember also, as all who have moved know, you can also stand the sofa
on its end.

[1] You may also slide down the bannister, if you wish.

[2] Don't forget though, this is actually the length of the longest
line segment that can be gotten around the corner; your sofa has
a non-zero width, also!