Square Root Mystery
Have you ever tried finding the square root of a number using a calculator and pressed the square root button more than once accidently well it happened to me once and I pushed it 50 times more in frustration.
I noticed something interesting
Ques 1) What did i notice?
Ques 2) Can you explain this?
- Sachin
I noticed something interesting
Ques 1) What did i notice?
Ques 2) Can you explain this?
- Sachin
Labels: SharedPuzzle
posted by Rajesh Lal at
10:13 PM
12 Comments:
I'm quite surprised that you didn't expect this, Raj. Remember Limits?
Although we have debates on here all the time about infinity, and whether its a number or not, that is irrelevent here. For the purposes of determining limits (asymptotic or other equation behaviors as the variable in ab equation increases indefinitly) infinity is a value and it can be represented as 1/0.
the equation sqrt(n), as we know, is n^(1/2). n^(1/2)^(1/2) is n^(1/4), and as such taking the square root x times can be represented as n^(1/(2^x)).
to find the limit of n^(1/(2^x)) power is simple: as X approaches infinity, 2^x also approaches infinity. therefore the equation approaches n^(1/oo) [im using oo to represent infintiy], which I said earlier is the same as n^(1/1/0) which is the same as n^0. Thus, the answer is ____.
I'll leave that one for the second poster.
That's me!
The answer is 1.
Sitting around, punching the square root button 50 times... I bet you noticed you need to get a life. :-)
The LIMIT you reached was the limits of your calculator.
True, it will approach 1, but never reach 1 exactly.
If your calculator could show decimals to infinity, it would never be exactly one.
hjg
My calculator shows 'stack error' at 25 square roots, at 24 it is very close to one but not exactly one.
just thought i would show what i got
you must have a much larger calculator then mine for it to do 50 square roots
Your "stack error" means that there are too many operations that your calculator cannot handle. What is being done here is sqrt(answer) and pressing equals over and over. Your calculator should have an 'ans' button.
Ques 1) What did you notice?
That you have way too much time on your hands.
Ques 2) Can I can explain this?
Yes. You have way too muc time on your hands.
Thats easy! You took the square root of that square root and so and so.
The "way too much time" Anon has way too much time on his hands, but he's not smart enough to answer the questions. If he had a life, he wouldn't be hanging around in here making snide remarks, and if he was smart, he'd just answer the questions.
you noticed that it ended as a 1 (unless it is 0.something then it makes 0) but if you pick any number 1 or above and keep square rooting it you'll end up with 1 (and not 3.14159265353897932384626433832795024481971693993
Obviously he noticed that the number after 1. ( the decimal Part) was being approximately halved every sqrt.
This can be explained using
(a+b)^2=a^2+2ab+b^2
This means that
104^2= 10000+800+16
= 10816
If you square root 10816, you will get 104, or aproximately half of what you stareted with after the 1.
Note: Sqrt(1.0816)=1.04
ShinPence
square root is an intresting math mystery,some mentalist used it on their performances
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