       Re: Mathematica strange behaviour finding a cubic root

• To: mathgroup at smc.vnet.net
• Subject: [mg129130] Re: Mathematica strange behaviour finding a cubic root
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 17 Dec 2012 02:57:12 -0500 (EST)
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• References: <20121216060645.D7C256924@smc.vnet.net>

```(-1/2)^(2/3) // N

-0.31498 + 0.545562 I

((-1/2)^(1/3))^2 // N

-0.31498 + 0.545562 I

Solve[y^(3/2) == -1/2, y] // N

{{y -> -0.31498 + 0.545562 I}}

NSolve[y^(3/2) == -1/2, y]

{{y -> -0.31498 + 0.545562 I}, {y -> -0.31498 - 0.545562 I}}

Solve[y^3 == (-1/2)^2, y] // N

{{y -> -0.31498 + 0.545562 I}, {y -> 0.629961}, {y -> -0.31498 - 0.545562 I}}

((-1/2)^2)^(1/3) // N

0.629961

This last approach forces a real result rather than the principal root
of the original expression.

((-1/2)^2)^(1/3) == (y /.
Solve[y^3 == (-1/2)^2, y, Reals][]) // Simplify

True

Bob Hanlon

This last approach forces a real result rather than the principal root
of the original expression.

On Sun, Dec 16, 2012 at 1:06 AM,  <sergio_r at mail.com> wrote:
>
> How can I make Mathematica provides the same answer for
> (-1/2)^(2/3) = ((-1/2)^2)^(1/3) ?
>
> What follows is a Mathematica session:
>
> In:= (-1/2)^(2/3)
>
>            1  2/3
> Out= (-(-))
>            2
>
> In:= N[%]
>
> Out= -0.31498 + 0.545562 I
>
> In:= ((-1/2)^2)^(1/3)
>
>          -(2/3)
> Out= 2
>
> In:= N[%]
>
> Out= 0.629961
>
>
> Sergio
>

```

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