`t` to the 1/8th power
Math brain teasers require computations to solve.
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.
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
Phyllis
Feb 01, 2001
 What is a rooth? 
jmanheim
Feb 02, 2001
 Your second sentence is syntactically incorrect. 
thephirm
Oct 18, 2001
 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. 
canu
Jul 13, 2004
 The words in the teaser look like English words, but put together they have no meaning in English or in math. 
Sane
Mar 20, 2005
 I did the subtraction wrong and came out with:
1/100 000 000
0.00000001

darthforman
May 25, 2005
 
stephiesd
Dec 09, 2005
 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. 
mr_brainiac
Jan 11, 2006
 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 ... 
lessthanjake789
Jan 29, 2006
 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 
Methlos
Mar 12, 2006
 I thing i might put my head under a pillow for a while 
Brainy_1
Mar 18, 2006
 That hurt my head! Nice job though! 
MadDog72
Mar 23, 2006
 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. 
Krystle
Jul 23, 2006
 wow, i'm not good at math at all 
Qrystal
Jul 29, 2006
 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. 
Qrystal
Jul 29, 2006
 eeek my answer got invaded by sunglass dudes!
That should say:
Let A = cos[pi/8]. Let B = sin[pi/8]. 
dimez_00
Oct 22, 2006
 i figured this:
(t+1)t=? ?^1/8 therefore i got
t+1t=1 1^1/8=the 8th root of 1 which is 1 
ChristheGreat
Nov 12, 2006
 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! 
EA_KLEIN
Mar 15, 2007
 whoever wrote this has some loose marbles in his keppie 
jamesbond
Apr 19, 2007
 ya ryt 
SRB_1807
Aug 17, 2011
 I love 2 eat ducks.. 
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