Math Help Thread - Page 3 - Politics Forum.org | PoFo

Wandering the information superhighway, he came upon the last refuge of civilization, PoFo, the only forum on the internet ...

Questions and research help requests. Student surveys may be posted here.
User avatar
By Smertios
#14098206
That's because cube roots don't have one single result.

Replace (-27) by x there. What you get is x^(-1/3), which is equal to 1/[x^(1/3)], right? That's 1 over the cube root of x:

Image = Image

The cube root of -27 is not -3. At least not only -3.

Image = Image = Image = Image

Now we have to define how much Image is equal to. To solve that, we need to solve the following equation: Image, where b is -1 and a is Image.

The solution of that equation gives us not one, but three complex results:
  • First result: a = -1
  • Second result: a = Image
  • Third result: a = Image

Depending on how you ask, Google gives you -0.333... as a result, as you were expecting. But that's just one of the possible results.

The ‘i’ you got is from the imaginary portion of the complex number. 0.166666667 - 0.288675135*i is a complex number, equal to what you get using the third result of ‘a’ given here. Only of of those 3 solutions is real (real numbers have only 1 cube root). The other two are complex numbers. In case you are not familiar with the complex set, please take a quick look at this.

There is an explanation here.
User avatar
By Seeker8
#14098243
Ah that explains it. i was doubting my self when google was giving me a different result but it seems we were both correct.

You're explanation was great, although i can't see how to get the 3 results from that equation. But i'm getting ahead of my self because i'm using khan academy and i haven't yet got to polynomials, quadratic functions and complex numbers. I prefer using khan to wikipedia as the latter isn't very noob friendly for technical subjects.

Thanks.

Not even @wat0n denies that the IDF and Israeli[…]

^ Wouldn't happen though, since the Israelis are n[…]

I was actually unaware :lol: Before he was […]

Israel-Palestinian War 2023

Every accusation is a confession Why sexual v[…]