/sci/ - Science & Math

>>11381169
so some math sperg can giz all over his own glasses

square root of x = x^(1/2)

>>11381169
actually decimal power functions occur in thermodynamics frequently, just off the top of my head.

>>11381169
das not tru tho faggot
>(expt (sqrt 2) (/ (sqrt 2)))
>1.2777038

>(expt (sqrt 2) (sqrt 2))
>1.6325269

Sqrt(x)= x^1/2
Then
If you have 2^(1/ sqrt(2)) multiply and divide the exponent with sqrt(2) then u have 2 ^ ( sqrt(2) /2) =
sqrt(2)^(sqrt(2))

>>11381204
Prove it. No calculator allowed.

>>11381169
take the sqrt(2)th root of 2. The LHS is just expressing that in mathematical symbols, and you get the RHS by expressing 2 as sqrt(2)^2, so, when you take the sqrt(2)th root of this, you get sqrt(2)^(2/sqrt(2)) = sqrt(2)^sqrt(2).

>>11381204
you aren't taking the sqrt(2)th root of sqrt(2) dumbfuck, you are taking the sqrt(2)th root of 2.

it's a transcendental number, that's why

>>11381169
[math] \displaystyle
\sqrt[ \sqrt{2}]{2}
=2^{ \frac{1}{ \sqrt{2}}}
=2^{ \frac{ \sqrt{2}}{2}}
=2^{ \frac{1}{2} \sqrt{2}}
= \sqrt{2} ^{ \sqrt{2}}
[/math]

>>11381541


>2√2√=212√=22√2=2122√=2√2

thats a nice proof

>>11381169
because on the left hand side you're using notation that shouldn't exist in the first place

>>11382954
found the idiot

>>11382954
Roots shouldn't exist in the first place, it's redundant.

>>11381169
QED

>>11383441
you haven't proved shit
>proof done backwards
>no justification from first to second RHS
>sideways fucking picture

>>11383441
this is garbage. a proof must begin from one expression and end in another with every step of the way justified

>>11383900
so which line fails?
erry line looks valid to me

>>11381541
/thread

>>11383915
>which line fails
your reading comprehension fails, I never said a line failed. read again

>>11383973
>I never said a line failed
ok good

>>11383978
while not a line fails, it means nothing when the finished product is not a proof of what you set out to prove. not good in the slightest

>>11384059
actually now that I look at your proof (I didnt care before I just gave you the benefit of the doubt), the second line doesnt even look right. The right side of the second line is ambiguous with its garbage notation and the original equation isnt even true btw, here is the proof that its false

[math] \sqrt{2}^{1/\sqrt{2}}[/math]

[math] (2^{1/2}) ^ {1/\sqrt{2}} [/math]

[math] (2^{1/2}) ^ {1/\sqrt{2}\cdot \sqrt{2}/\sqrt{2}} [/math]

[math] (2^{1/2}) ^ {\sqrt{2}/2} [/math]

[math] 2 ^ {\sqrt{2}/4} [/math]

and since sqrt(2)/4 is not equal to sqrt(2)/2, by uniqueness of prime factorization, the original statement is false

>>11384082
gaze upon this, ye mighty, and despair

>>11384085
not only have I proven that it is false, if you are a numerical brainlet here you go. also, wolfram alpha gets many things wrong its not even worth using that garbage.

>>11384082
topkek, found the idiot

>>11384098
look here, you faggot

>>11384103
how am I an idiot? I am of course assuming that the notation of a_sqrt(b)=b^(1/a). there is not fault in my logic, proof, or the numerical approximation under this assumption...

>>11384107
see >>11384106

>>11384106
a_sqrt(b)=b^a?

>>11384098
oh wow so 1.41421356237
isn't equal to 0.70710678119
and that is supposed to prove you right?
holy shit you're stupid

>>11384117
>>11384082
dont make yourself sound stupid, thats the last thing we would want

>>11384098
>>11384106
compare decimal values between these two posts

>>11384124
youre relying on a computer which says sqrt(2)_sqrt(2)=sqrt(2)^sqrt(2) but im not sure how this is the case (for a_b, _ here means a is put up behind the square root as your picture indicates)

>>11384120
says the retard who has the lower 2 under a root for no reason in >>11384098
do you piss in your cereal?

>>11384133
I dont have any more time to waste on your brainlet engineering antics. Ive given the proof and all youve done is shown a picture of wolfram. who is the real brainlet here

>>11384138
you gave W-A the wrong thing to calculate you absolute fart

>>11384146
math is not done is wolfram alpha its done on paper with proofs. the only uncertainty is the notation you are using where you bring the sqrt(2) up behind and to the left of the square root bracket.

>>11384149
the lower line in >>11384098
should be 2^blahblah
NOT sqrt(2)^blahblah
now finish your cereal

>>11384153
2^1/2 is the same thing as sqrt(2).

>>11384156
blahblah =/= 1/2

>>11381617
for you

>>11384157
FUCK youre right. jesus christ im an autist. apologies

>>11381204
lmao, pathetic

>>11384098
>tfw not living the mathematical lifestyle

>>11381541
first equality is dead wrong, as is therefore the rest. the equation does not hold btw, sqrt 2 is greater than 1, so the exponential function having it for base is strictly increasing and sqrt 2 is strictly greater than 1/sqrt 2.

>>11383593
>>11383900
It’s proved by basic algebra, go back to elementary school

>>11384923
>first equality is dead wrong
[citation needed]

>>11384923
https://en.wikipedia.org/wiki/Nth_root#Identities_and_properties

>>11384942
Not saying the statement isn't true, just saying his pic is a fail, and thus giving him shit for it, as we do on /sci/

>>11381541
based trole

>>11385028
>yoloooo we are the kul kids djuuude he is vertical filming lets make fun of this Loser haha that’s what we do
You must be older than 18 to post here

>>11385060
how is it a troll? that is a valid proof moron

>>11381169
Because 1/root(2) = root(2).

>>11381541
>1/sqrt(2) = sqrt(2)/2
Prove it faggot.

>>11385830
multiply with 1
oh right, forgot that you're an idiot
>out comes crayons and sock puppet
multiply with sqrt(2)/sqrt(2)

Desmos is retarded.

>>11387143
> x^x
topkek, thanks for the laugh

I can't tell whether half the posts here are bait or people are just idiotic.

>>11381169
because 1/sqrt(2)=sqrt(2)/2 go to school

>>11381194
why? please show me it sounds dope

>>11387143
You forgot a squareroot right after the -

>>11387143
>>11387611
or rather 3 squareroots (one around each of the "x"es)

>>11384098
>wolfram alpha gets many things wrong its not even worth using that garbage
no, you made a blatant mistake

>>11387143
>Desmos is retarded.
no, you made a blatant mistake

pathetic

>>11381169
[eqn] \sqrt[\sqrt2]2 = 2^{\frac{1}{\sqrt2}} = 2^{\frac{1}{2}\cdot\frac{2}{\sqrt2}} = (2^\frac{1}{2})^\frac{2}{\sqrt2} = \sqrt2^{\frac{2}{\sqrt2}} = \sqrt2^\sqrt2 [/eqn]
if you can't do basic algebra please just gtfo this board

>>11387708
I never realized x/sqrt(x) equals sqrt(x), what the fuck

>>11385830

good thread

Imagine being pleb filtered by fucking grade school level math.