/sci/ - Science & Math

Index laws, mayne.

2=2^(1)=2^(1/2*2)

multiply it by sqrt(2)

2^2*2^2=2^4
2^3*2^3=2^6
2^0.5*2^0.5=2^1=2

Dunno if you're looking for some deeper theoretical meaning but the trivial highschool algebra proof would be something like
<span class="math">\frac{2}{\sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \frac{\sqrt{2}}{1} = \sqrt{2} [/spoiler]
Since you can always multiply by any form of 1 without changing the value, and then just reduce the fraction.

>>3986259
...why the fuck did i make the same step twice with no advancement further towards the answer??
fucks sake!

(2^1)/(2^(1/2)) = 2^(1 - 1/2) = 2^(1/2) = sqrt(2)

if you know exponential numbers , here is a proof using em
sqrt(x) = x^1/2
if you divide two exponational numbers,you just subtract the numbers on top
so
2 = 2^1
sqrt(2) = 2^1/2
2^1 / 2^1/2 = 2^1/2

rationalizing denominators was taught in algebra. and I think I stopped doing it around trigonometry because who gives a shit about radicals on the bottom

All of your proofs are clunky.
Think about what sqrt(2) actually IS, and no proof is required.

I actually facepalmed.
Good job OP

>>3986281
>Think about what sqrt(2) actually IS
What is it?

>All of your proofs are clunky.
>no proof is required.
precalculus fag detected

Never worry, OP. Everything can be derived from whole numbers.

>Let m/n = sqrt2
>Either m or n is an odd number
>m^2 = 2n^2
>Hence, m^2 is an even number
>That means m can only be an even number
>Let, m = 2k
>(2k)^2 = 2n^2
>4k^2 = 2n^2
>2k^2 = n^2
>n^2 is an even number

Wait, what.
But, m and n cannot be even numbers at the same time. Than that means not everything can be derived from whole numbers. Then that means absolute clarity will always remain nebulous!!!

Brb,suicide.

>>3986297
is that really the proof they discovered? I always figured it would be more geometric and less... modern.

>>3986297
It's like first year algebra all over again!

>>3986297
This is like one of those brainfucks where they secretly devide by 0

>let m/n = some irrational number

>>3986318
>I am in high school trigonometry and have never heard of an indirect proof

Because
sqrt(2) * sqrt(2) = 2
Therefore:
sqrt(2) = 2/(sqrt 2)

>>3986248
10/10