Logic question

[83hurstguy]

So, I just got out of one of my Mech Eng finals.... Anyone here know the last answer to the test? this is all it said:

True or False

1 = sqrt(1) = sqrt(-1*-1) = sqrt(-1)*sqrt(-1) = j * j = -1

(sqrt is square root, representing a radical... j can also be referred to as i)

 

[The Blob]

Is that a trick question? It seems to boil down to 1 = -1... which would obviously be false.

And there is no such thing as sqrt -1 unless there's some kind of quantum physics type situation where it could exist.

 

[83hurstguy]

j (or i) is called an irrational number...

sqrt(-1) = j... sqrt(-4) = 2j

j*j = -1, j*j*j = -j , j^4 = 1, j^5 = j once again and the cycle repeats... they actually teach this in high school freshman year algebra these days.

is it a trick question? most likely... its apparently true, but nobody knows either way.

 

[The Blob]

...they actually teach this in high school freshman year algebra these days.

Why?

...its apparently true, but nobody knows either way.

If you can get the teacher's explanation for it being true, please post it. It still seems to me that the equation is saying that all those things are equal and all those things include 1 and -1. So, unless you live in Bizzaro world, it can't be true.

 

[Brian Collins]

It has to be false because 1 does not equal -1. The question is where the error is.

I think the problem is sqrt(-1*-1)=sqrt(-1)*sqrt(-1)

In the left side, the -1 in multiplied before the root is taken, so it's really just the sqrt of 1.

In the right side, the root is taken before the negative in cancled out.

BTW, I think that "i" or sqrt(-1) is a non-real number. An irrational number is a non-repeating, non-terminating decimal.

But what do I know? I failed calc twice and had to join the military. Thanks for giving us something to thing about.

 

[83hurstguy]

non-real thanks for catching my error

anyways... sqrt(-1 * -1) should equal sqrt(-1)*sqrt(-1)...

works with other numbers: sqrt(9*4) = sqrt(9)*sqrt(4) (both equal 6).

I agree with ya though, don't see how its possible; square roots are designed to work with positive numbers, it just goes to show there is a glitch in a theory somewhere, lol.

 

[GNandGS]

How fast is the belt moving?

 

[PCS74]

Brian has it right.

(-1*-1) = 1

sqrt(-1*-1) = sqrt(1)

sqrt(-1*-1) is not equal to sqrt(-1)*sqrt(-1)

Chris S

 

[salvageV6]

sqrt(-1*-1) = sqrt(-1)*sqrt(-1)

You can't take things in parenthesis and then move them outside without consulting your lawyer and Stephen Hawking.

Now go roll a j or buy an old TI calculator and test it out.

 

[Brian Collins]

-"anyways... sqrt(-1 * -1) should equal sqrt(-1)*sqrt(-1)...

works with other numbers: sqrt(9*4) = sqrt(9)*sqrt(4) (both equal 6)."

that's a good point, but the issue is with the signs not the number.
Consider this:

i=sqrt(-1)

sqrt(-9*-4)= sqrt(36)= +/-6 (can be eaither positive or negative)

sqrt(-9)*sqrt(-4)=i sqrt(9) * i sqrt(4)= i^2* +/-3*+/-2= -1*+/-3*+/-2

From here it could go four ways. (+3 & +2)(+3 & -2)(-3 & +2)(-3 & -2)

-1*3*2=-6
-1*3*-2=6
-1*-3*2=6
-1*-3*-2=-6
so +/-6 is the answer. Kinda shot my self in the foot here


hum... going back to the original question. I still think it's wrong because 1 does not equal -1. The trick is that both one and negative one are possible solutions for the sqrt(-1*-1).

Let us know what the teacher says.

 

[turbo buicks]

isnt the problem with the 2nd equation? sqrt(-1 * -1). the problem distributes the sq root but if this equation was alone wouldnt you follow the P.E.M.D.A.S. rule and solve the parentheses prob 1st making it sqrt(1)=1 is distributing a sqrt allowed or is that only numbers? even so, couldnt you sorta FOIL it making it i*i*i*i = 1 therfore 1=1

 

[Brian Collins]

sqrt(1) does not only equal one, it is also equal to -1.
Remember that 1*1=1 and also -1*-1=1

So I could say that "1=sqrt(1)=-1" and looking at only one side (ignoring eaither the 1 or -1) at a time the equation seems true. I think the correct way to express this is sqrt(1)=+/-1.

 

[DavzGN]

It's false.

because sqrt(-1) has no value. you cannot square any number and get a negative number, so -1 doesn't have a square root.

HTH
David

 

[Brian Collins]

Sqrt(-1)equals a number, just not a real number. It's a non-real number expressed as i. I don't remember why they are non-real numbers but there is a reason.