### Brain Teasers

# `t` to the 1/8th power

How might a mathematician describe a number `t` held to the following condition:

When (t+1) is subtracted from t and the result is raised to the 1/8th power.

When (t+1) is subtracted from t and the result is raised to the 1/8th power.

### Answer

Imaginary Number.Whenever (t+1) is subtracted from `t`, you will simply be left with -1. -1 raised to the 1/8th power is the same as taking the positive root of something. When taking the positive root of any negative number, you are left with an imaginary number.

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## Comments

What is a rooth?

Your second sentence is syntactically incorrect.

Your claim that taking the positive root of any negative number results in an imaginary number is incorrect. For example, the cube root of -1 is -1 (-1 * -1 * -1 = -1). However the even root of any negative number will be imaginary.

The words in the teaser look like English words, but put together they have no meaning in English or in math.

I did the subtraction wrong and came out with:

1/100 000 000

0.00000001

1/100 000 000

0.00000001

i read it wrond after i did the subtraction, i read it as the -8th power, resulting in -1.

anyhow, we haven't covered imaginary numbers yet. i think they're next chapter.

anyhow, we haven't covered imaginary numbers yet. i think they're next chapter.

I don't think that the answer is really an imaginary number, I think it's more likely an imaginary imaginary number, or maybe it's an imaginary imaginary imaginary number, or maybe it's ...

wrong... all of you. the number t is a positive, real number. let t = 100, t+1 = 101. t-(t+1) = -1, raised to the 1/8th is, truly an imaginary number, but as you can see, "t" is ANY real number, positive or negative. sorry, but poorly thought out teaser

I thing i might put my head under a pillow for a while

That hurt my head! Nice job though!

I see four problems with this teaser:

1) It asks for the number t, not the value of (t-(t+1))^(1/.

2) Why bother with t? Isn't it obvious that if t+1 is subtracted from t, the result is -1?

3) The answer is vague. I actually computed the answer, only to find that all you wanted was 'imaginary'.

4) It's not an imaginary number! An imaginary number is a number of the form b*i, where i^2=-1. The answer is of the form a + b*i, where a is nonzero (there are actually 8 answers, but they are all of this form). The answer is complex and not real, but not imaginary either.

1) It asks for the number t, not the value of (t-(t+1))^(1/.

2) Why bother with t? Isn't it obvious that if t+1 is subtracted from t, the result is -1?

3) The answer is vague. I actually computed the answer, only to find that all you wanted was 'imaginary'.

4) It's not an imaginary number! An imaginary number is a number of the form b*i, where i^2=-1. The answer is of the form a + b*i, where a is nonzero (there are actually 8 answers, but they are all of this form). The answer is complex and not real, but not imaginary either.

wow, i'm not good at math at all

I figured that a mathematician would call 't' TRIVIAL. After all, it got subtracted out of the situation right away.

There must be a way this teaser could be improved so that it asks what it means to ask... although of course MadDog72 is absolutely correct in stating that [-1]^[1/8] is technically considered complex, not imaginary.

Does anyone care that [-1]^[1/8] has 8 answers?

Let A = cos(pi/. Let B = sin(pi/.

Then [-1]^[1/8] =

( A + B*i, B + A*i, -B + A*i, -A + B*i,

-A - B*i, -B - A*i, B - A*i, A - B*i )

Anyways, I don't care if anyone else doesn't care; I wrote it because I care. So there.

There must be a way this teaser could be improved so that it asks what it means to ask... although of course MadDog72 is absolutely correct in stating that [-1]^[1/8] is technically considered complex, not imaginary.

Does anyone care that [-1]^[1/8] has 8 answers?

Let A = cos(pi/. Let B = sin(pi/.

Then [-1]^[1/8] =

( A + B*i, B + A*i, -B + A*i, -A + B*i,

-A - B*i, -B - A*i, B - A*i, A - B*i )

Anyways, I don't care if anyone else doesn't care; I wrote it because I care. So there.

eeek my answer got invaded by sunglass dudes!

That should say:

Let A = cos[pi/8]. Let B = sin[pi/8].

That should say:

Let A = cos[pi/8]. Let B = sin[pi/8].

i figured this:

(t+1)-t=? ?^1/8 therefore i got

t+1-t=1 1^1/8=the 8th root of 1 which is 1

(t+1)-t=? ?^1/8 therefore i got

t+1-t=1 1^1/8=the 8th root of 1 which is 1

Hmm.. you did't include the fact that pi to the 3rd power minus the radius of a duck's butt plus the deepness of a toilet = 5 times the 3rd trigonometric function plus the amount of time it takes for the final star to impact the earth causing free cake for everyone!

whoever wrote this has some loose marbles in his keppie

ya ryt

I love 2 eat ducks..

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