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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-

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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"]
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  • $\begingroup$ 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. $\endgroup$ – Luca Mar 11 '15 at 20:49
  • $\begingroup$ @Luca x^y is shorthand for Power[x, y], so both should work. $\endgroup$ – Chip Hurst Mar 12 '15 at 21:46
  • $\begingroup$ Yes, you are right, it works also with Power[] function. Thank you Chip. $\endgroup$ – Luca Mar 17 '15 at 21:38

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