# How do I get a numerical cube root?

**URL:** <https://community.wolfram.com/t/how-do-i-get-a-numerical-cube-root/2236>\
**Category:** Questions\
**Tags:** mathematica\
**Created:** [May 18, 2014, 10:45am UTC](https://community.wolfram.com/t/how-do-i-get-a-numerical-cube-root/2236 "2014-05-18T10:45:32Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![apes](https://avatars.discourse-cdn.com/v4/letter/a/73ab20/32.png) [@apes](https://community.wolfram.com/u/apes)\
**Post date:** [May 18, 2014, 10:45am UTC](https://community.wolfram.com/t/how-do-i-get-a-numerical-cube-root/2236/1 "2014-05-18T10:45:32Z")

</div>

Hi  
Can’t paste code on my machine.

Input

\.b2r = CubeRoot[((¹V)/Pi ) (3/4)]; (\* need cube root of \.b2r 3Sqrt[\.b2r] \*)

Out put

“\.b2r =” Surd[Quantity[5.46439\*10^-69, (“Meters”)^3], 3]

I require a numerical value like 1.8 x 10^-23 meters

PS 1V is a calculated volume, but any cube root will do.  
Many Thanks  
Andrew Pepes

---

<div class="post-metadata">

**Author:** ![mthiel](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/mthiel/32/42877_2.png) [@mthiel](https://community.wolfram.com/u/mthiel)\
**Post date:** [May 18, 2014, 11:25am UTC](https://community.wolfram.com/t/how-do-i-get-a-numerical-cube-root/2236/2 "2014-05-18T11:25:04Z")

</div>

Would something like this work?

```auto
Power[Quantity[5.46439*10^-69, ("Meters")^3], 1/3]

```

It gives

```auto
Quantity[1.76136*10^-23, "Meters"]
(* 1.76136*10^(-23) m *)

```

M.

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<div class="post-metadata">

**Author:** ![apes](https://avatars.discourse-cdn.com/v4/letter/a/73ab20/32.png) [@apes](https://community.wolfram.com/u/apes)\
**Post date:** [May 18, 2014, 2:44pm UTC](https://community.wolfram.com/t/how-do-i-get-a-numerical-cube-root/2236/3 "2014-05-18T14:44:30Z")

</div>

Hi Marco

Brilliant, I used it with my variables

```auto
 \.b2r = Power[Quantity[((¹V)/Pi ) (3/4)], 1/3];

```

and it gives

```auto
"\.b2r =" (Quantity[1.76136*10^-23, "Meters"])

```

Many Thanks

---

<div class="post-metadata">

**Author:** ![lucaivaldi75](https://avatars.discourse-cdn.com/v4/letter/l/ce7236/32.png) [@lucaivaldi75](https://community.wolfram.com/u/lucaivaldi75)\
**Post date:** [March 7, 2015, 10:10am UTC](https://community.wolfram.com/t/how-do-i-get-a-numerical-cube-root/2236/4 "2015-03-07T10:10:13Z")

</div>

Hi, I’m very new to Mathematica and I can’t figure out how power simplifications are performed.  
If I try with

```
N[Power[Quantity[4, ("Centimeters")^3]*3/4/Pi, 1/3], 3]

```

I get 0.985 cm which is what I expect.

But, if I try with something like

```
Clear[r1, r2, v1, v2];
r1 = Quantity[2 , "Centimeters"]
v1 = r1^3*3/4*Pi
v2 = v1*5
r2 = N[CubeRoot[v2*3/4/Pi], 2]

```

I get

```
Surd[Quantity[45/2, "Centimeters"^3], 3]

```

where I would expect CubeRoot[“Centimeters”^3] to be simplified to “Centimeters”.

What am I doing wrong?

Thank you for your help,  
Luca-