How can I express SQRT(27) in terms of i and cancel out the i?

[GreenPrint]

Homework Statement

I was trying to do this problem and noticed that I should be able to express SQRT(27) in terms of i and cancle out the i making it more simple I can't seem to remember how to do this thanks

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Homework Equations

The Attempt at a Solution

 

[GreenPrint]

here you go sorry about that

[PLAIN]http://img294.imageshack.us/img294/5396/captureow.jpg

i need to solve for x don't remeber how to do this

 

[GreenPrint]

well i think i got this afterall maybe?

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nope dang let me see what i did wrong here

 

[Mark44]

If you're looking for the solutions to x² - 27 = 0, they are the real numbers x = 3\sqrt{3} and x = -3\sqrt{3}. Otherwise, I have no idea what you're trying to do.

 

[GreenPrint]

I think i may have just proved
SQRT(27) = -27
did something wrong but I did it step by step let me look at this :(

 

[GreenPrint]

I'll show you in a moment I think i may have just proved SQRT(27) = -27
I don't think I have done anything wrong this is really weird let me type it up... hope I'll find something wrong because if i don't... :O

 

[GreenPrint]

I'm trying to find the form of SQRT(27) that will allow me to simplify it furhter

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as you can see I don't know were i went wrong I'm trying really hard to find it I typed it up so you could see hwat I did step by step

 

[GreenPrint]

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Well I went through Euler's original derivation of the trignometic functions for sine and guess i just missed up some where but got it right some how

ok...

and then ummm crap...

I started from the top

 

[GreenPrint]

but you that form is better to use becasue then you can cancel out the pi and your left with i raised to some fraction much easier to evalute no? but you i guess i misse dup some where and did it wrong but it works

 

[GreenPrint]

well that sure is strange I never was taught that form of sin I just wen through the derrivation i guess of euelr's sine formula and screwed up somewhere but it's right

wounder why I have never encountered it before i think it would be much easier to use no

 

[GreenPrint]

I think I have messed up when I did SQRT(3) as an example sorry

 

[GreenPrint]

Well see what I think I need to do is take my sine equation and set it equal to sqrt(37) sine can take on any value those who say it's llimited betweeen 1 and negative one are liers... and then solve so when solved earlier I think I was doing it right I thinkI just need to start over

 

[GreenPrint]

well i guess in theory I should have just done this

http://img706.imageshack.us/img706/4708/capturefeb.jpg

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and solved for x since sine can take on any value it wants then just do sin(x) would truly be the most simplifed huh?
I think that would be a better way to do it instead of setting it equal to sqrt(27) yes I know realize I forgot the initial 1/2 when I original atempted and set it eqaul to sqrt(27) so should i set it equal to sqrt(27) or just the whole darn thing

 

[GreenPrint]

I take that back what I originally did wasn't wrong as that should be able to take on any number that it desires as well no and then I could cancel out the i if I had one in the denomenator, in post number seven I guess I just did something wrong...

 

[GreenPrint]

well i just had this great idea that I'm going to work out tommarow I am going to set cosine=sine
yes that's
cos(x)=sin(x)
or in common terms what angle does cosine and sine have the same value... none? Don't think so my friend I'm not buying it... I just woundering what will happen I am going to solve it...

sorry by the way i started out trying to do that problem then got into sine and this idea just poped into my head and was like well i should be able to solve that technically speaking...

well i just did it everything canceled out I wounder what that means oh crap maybe you guys were right there is none =(

 

[Mark44]

I think i may have just proved
SQRT(27) = -27

This is ridiculous. If this were true, the 27 = (-27)² would also be true. Obviously, it isn't.

sqrt(27) is not a complex number, so why are you even bothering to go down that path?

In its simplest form, sqrt(27) is 3sqrt(3).