(-1)^(2/3) = ?

[speg]

My dosn't my calculator give me an answer? I thought it was 1, and my text book says it's one. But my calculator says it's error 2 😕

 

[minendo]

The answer is one. Depends on where you put the negative in your calculator.

 

[NogginBoink]

Calc.exe gives "Invalid input for function."

That's the first time I've ever seen calc.exe give an error!

 

[notfred]

your calculator must suck because mine says 1.

 

[Haircut]

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

Your calculator probably tried to do it using logarithms, thus giving you the error

 

[tigerbait]

my brain calculator says 1

 

[PrincessGuard]

(-1)^(2/3) = [(-1)^2]^(1/3)

Doh, beat to the punch.

 

[Kyteland]

Originally posted by: speg
My dosn't my calculator give me an answer? I thought it was 1, and my text book says it's one. But my calculator says it's error 2 😕

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

((-1)^(1/3))^2 = -1/2+sqrt(3)/2*i

(-1)^(0.6666...) = -1/2+sqrt(3)/2*i

0.9999... = 1

 

[zippy]

TI-83+ is telling me 1. 🙂

Dude, did you seriously need to put that into your calculator to figure out though?! :Q

 

[speg]

This calculator sucks, not the first time it's been sucky either 🙁 I want my old one back, someone stole it last semester though :frown: Thanks guys, at least I'm not going crazy 😉

 

[speg]

Originally posted by: zippy
TI-83+ is telling me 1. 🙂

Dude, did you seriously need to put that into your calculator to figure out though?! :Q

It was part of a larger equation, so I had typed the whole thing into my calculator, resulting in the error 2. So I isolated the (-1)^(2/3) as the part that was messing up my calculator.

 

[Kyteland]

Originally posted by: zippy
TI-83+ is telling me 1. 🙂

Dude, did you seriously need to put that into your calculator to figure out though?! :Q

My HP 48G is telling me it is -1/2+sqrt(3)/2*i and everybody knows that it is a far superior calculator than the TI-83 (or any TI for that matter...) 😉

 

[Anubis]

my Ti-83 says 1

so does Mathamatica and Maple

 

[Kyteland]

but to actually answer your question:

(-1)^(2/3) = Y
(-1)^2 = Y^3
1=Y^3

try Y=1
1^3 = 1
which works

try y = -1/2+sqrt3/2*i
(-1/2+sqrt3/2*i)^3 = (-1/2+sqrt2/2*i)*(-1/2+sqrt2/2*i)*(-1/2+sqrt2/2*i)
(-1/2+sqrt3/2*i)^3 = -1/8+3*sqrt3/2*i - 9/8*i^2 + 3*sqrt3/2*i^3
(-1/2+sqrt3/2*i)^3 = 1
which also works

Both are correct answers

 

[TuxDave]

Originally posted by: Kyteland

Originally posted by: speg
My dosn't my calculator give me an answer? I thought it was 1, and my text book says it's one. But my calculator says it's error 2 😕

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

((-1)^(1/3))^2 = -1/2+sqrt(3)/2*i

(-1)^(0.6666...) = -1/2+sqrt(3)/2*i

0.9999... = 1

lol

 

[dabuddha]

Originally posted by: Kyteland

Originally posted by: zippy
TI-83+ is telling me 1. 🙂

Dude, did you seriously need to put that into your calculator to figure out though?! :Q

My HP 48G is telling me it is -1/2+sqrt(3)/2*i and everybody knows that it is a far superior calculator than the TI-83 (or any TI for that matter...) 😉

true but the HP48GX > HP 48G 🙂

 

[notfred]

Originally posted by: Kyteland

Originally posted by: zippy
TI-83+ is telling me 1. 🙂

Dude, did you seriously need to put that into your calculator to figure out though?! :Q

My HP 48G is telling me it is -1/2+sqrt(3)/2*i and everybody knows that it is a far superior calculator than the TI-83 (or any TI for that matter...) 😉

Apparently it's not.

 

[jteef]

My TI-85 says (-.5 + 0.866j) maybe i've dropped it too many times