# Simplify CubeRoot of meter cubes

Why Mathematica doesn't simplify CubeRoot of meter cubes to meters?

r = Quantity[10, "Meters"];
v = 4/3 r^3 Pi;
CubeRoot[% * 3/4 / Pi]


returns

Surd[Quantity[1000, ("Meters")^3], 3]


instead of 10m, which was what I would expect. I think this has something to do with the fact that a the root could be a complex number. I searched the web and found some hints about using assumptions, but it didn't work for me. Please, could anybody help me to understand what I'm doing wrong?

Thank you, L-

It appears Surd is not integrated into Quantity (and it probably should be). This auto simplifies:
r = Quantity[10, "Meters"];

Quantity[10, "Meters"]

• @Luca x^y is shorthand for Power[x, y], so both should work. – Chip Hurst Mar 12 '15 at 21:46