# 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"];
v = 4/3 r^3 Pi;
(%*3/4/Pi)^(1/3)

Quantity[10, "Meters"]

• Thank you Chip for your answer. I didn't realize I could use ^ operator! Anyway I think it doesn't work with Power[] function too.
– Luca
Mar 11, 2015 at 20:49
• @Luca x^y is shorthand for Power[x, y], so both should work. Mar 12, 2015 at 21:46
• Yes, you are right, it works also with Power[] function. Thank you Chip.
– Luca
Mar 17, 2015 at 21:38