/sci/ - Science & Math » Thread #11189634

7KiB, 351x581, math_rationalize_1_div_sq2.png

View Same Google iqdb SauceNAO

Anonymous Sun 01 Dec 07:45:23 2019 No.11189634 View Reply Original Report

Quoted By: >>11189701 >>11189765 >>11189774 >>11189802 >>11189817 >>11190221 >>11192748 >>11192921 >>11193458

>Now rationalize the denominator!
No.

Anonymous

View Same Google iqdb SauceNAO 1575186323812.jpg, 23KiB, 351x581

Anonymous Sun 01 Dec 2019 08:44:20 No.11189701 Report

Quoted By:

>>11189634
>>Now rationalize the denominator!

ez

Anonymous

Anonymous Sun 01 Dec 2019 09:35:59 No.11189765 Report

Quoted By:

>>11189634
I hated this shit in geometry

Anonymous

Anonymous Sun 01 Dec 2019 09:40:47 No.11189774 Report

Quoted By: >>11190234 >>11193998

>>11189634
>he has no idea why we rationalize the denominator
not gonna make it.

Anonymous

Anonymous Sun 01 Dec 2019 09:52:03 No.11189802 Report

Quoted By:

>>11189634
>can't multiply by 1
The brightest mind

Anonymous

Anonymous Sun 01 Dec 2019 10:15:10 No.11189817 Report

Quoted By: >>11190533

>>11189634
>sqrt2*sqrt2
>= 2sqrt2
absolutely low IQ. At least you got the right answer at the end, probably by memorizing the correct answer and not by actually understanding the shit.

Anonymous

Anonymous Sun 01 Dec 2019 14:37:49 No.11190221 Report

Quoted By: >>11190898 >>11191180 >>11195433

>>11189634
But Anon, sqrt(2*2) could be -1!

Anonymous

Anonymous Sun 01 Dec 2019 14:43:06 No.11190234 Report

Quoted By: >>11191261 >>11194035

>>11189774
To make it harder to guess numerical approximations.

Anonymous

Anonymous Sun 01 Dec 2019 16:59:33 No.11190533 Report

Quoted By:

>>11189817
can you read?

Anonymous

Anonymous Sun 01 Dec 2019 19:42:20 No.11190898 Report

Quoted By: >>11191184 >>11194018

>>11190221
-2 I mean.

Anonymous

Anonymous Sun 01 Dec 2019 21:49:11 No.11191180 Report

Quoted By: >>11191184 >>11191245 >>11191290

>>11190221
no, it can't. the principal square root of something is defined to be non-negative

Anonymous

Anonymous Sun 01 Dec 2019 21:51:46 No.11191184 Report

Quoted By:

>>11190898
>>11191180

jesus the devil

jesus the devil Sun 01 Dec 2019 22:20:55 No.11191245 Report

Quoted By: >>11191285

>>11191180
>implying imaginary numbers dont exist

Anonymous

Anonymous Sun 01 Dec 2019 22:25:17 No.11191261 Report

Quoted By: >>11194035

>>11190234
>half of 1.4142... is harder to guess than one over 1.4142...
no

Anonymous

Anonymous Sun 01 Dec 2019 22:40:57 No.11191285 Report

Quoted By:

>>11191245
i didn't imply that. it's just how the principal square root is defined, that it always is non-negative: https://en.wikipedia.org/wiki/Square_root
>Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by ?x

Anonymous

Anonymous Sun 01 Dec 2019 22:45:12 No.11191290 Report

Quoted By: >>11191297 >>11191312 >>11191332 >>11192674 >>11194002

>>11191180
>defined
You mean you arbitrarily chose the nonnegative part and created consensus by saying 'it's defined as'?

Anonymous

Anonymous Sun 01 Dec 2019 22:49:18 No.11191297 Report

Quoted By: >>11191312 >>11192758

>>11191290
the symbols have a well-defined meaning

Anonymous

Anonymous Sun 01 Dec 2019 22:57:35 No.11191312 Report

Quoted By: >>11192758

>>11191290
i didn't do it personally, but, as said in this >>11191297 post, the symbols have a well-defined meaning

Anonymous

Anonymous Sun 01 Dec 2019 23:02:06 No.11191321 Report

Quoted By:

$1 = \frac{x}{x} = \frac{ \sqrt{x} \sqrt{x} }{x}$
so
$\frac{1}{\sqrt{x}} = \frac{ \sqrt{x} \sqrt{x} }{x}$

Anonymous

Anonymous Sun 01 Dec 2019 23:03:10 No.11191325 Report

Quoted By: >>11191339 >>11192710 >>11192931 >>11193454 >>11193461 >>11193966 >>11194005

$1 = \frac{a}{a} = \frac{ \sqrt{a} \sqrt{a} }{ a } \implies \frac{1}{\sqrt{ a }} = \frac{ \sqrt{ a } }{ a }$

redpill me on squat shoes

redpill me on squat shoes Sun 01 Dec 2019 23:05:47 No.11191332 Report

Quoted By: >>11192758

>>11191290
not anon himself, but yes that is pretty much what we did
and it is helpful in situations where imaginary numbers aren't useful

Anonymous

Anonymous Sun 01 Dec 2019 23:07:37 No.11191339 Report

Quoted By: >>11191352

>>11191325
\frac{ \sqrt{a} \sqrt{a} }{ a } \implies \frac{1}{\sqrt{ a }}
wtf. what's the joke? it's just wrong

Anonymous

Anonymous Sun 01 Dec 2019 23:13:21 No.11191352 Report

Quoted By: >>11191355

>>11191339
i meant
$\frac{ \sqrt{a} \sqrt{a} }{ a } \implies \frac{1}{\sqrt{ a }}$

Anonymous

Anonymous Sun 01 Dec 2019 23:14:28 No.11191355 Report

Quoted By: >>11191361 >>11191366

>>11191352
fuck
$$\frac{ \sqrt{a} \sqrt{a} }{ a } \implies \frac{1}{\sqrt{ a }}$$

Anonymous

Anonymous Sun 01 Dec 2019 23:15:33 No.11191361 Report

Quoted By: >>11192583

>>11191355
lol i give up

Anonymous

Anonymous Sun 01 Dec 2019 23:17:54 No.11191366 Report

Quoted By: >>11191372 >>11192710 >>11192931 >>11193454

>>11191355
$\frac{ \sqrt{a} \sqrt{a} }{ a } \implies \frac{1}{\sqrt{ a }}$

Anonymous

Anonymous Sun 01 Dec 2019 23:18:58 No.11191372 Report

Quoted By: >>11192583

>>11191366
yes! finally!

Anonymous

Anonymous Mon 02 Dec 2019 07:43:21 No.11192583 Report

Quoted By:

>>11191372
Doesn't make sense, a numberical expressions doesn't imply another>>11191361

Anonymous

Anonymous Mon 02 Dec 2019 08:38:04 No.11192674 Report

Quoted By: >>11192758

>>11191290
>definitions are arbitrary
I hate math now.

Anonymous

Anonymous Mon 02 Dec 2019 09:01:54 No.11192703 Report

Quoted By:

The destruction of Army Group Center

Anonymous

Anonymous Mon 02 Dec 2019 09:12:56 No.11192710 Report

Quoted By: >>11192931

this is true >>11191325
this doesn't make sense >>11191366

Anonymous

Anonymous Mon 02 Dec 2019 09:30:51 No.11192719 Report

Quoted By:

these problems along with solving for the difference quotient were what made me realize math is fun and satisfying

Anonymous

Anonymous Mon 02 Dec 2019 09:56:34 No.11192748 Report

Quoted By:

>>11189634
Yeah we stopped doing this in like middke school. Are you fucking 12?

Anonymous

Anonymous Mon 02 Dec 2019 10:02:59 No.11192758 Report

Quoted By: >>11192949

>>11191297
>>11191312
That's a meaningless statement.

>>11191332
>>11192674
These guys got it right. Although arbitrary is a bit harsh in most contexts. It's often guided by intuition of what makes sense. We chose the nonnegative part because the real root function is also undefined for negative numbers.

Anonymous

View Same Google iqdb SauceNAO IMG_20191202_130759.jpg, 52KiB, 495x659

Anonymous Mon 02 Dec 2019 12:08:25 No.11192921 Report

Quoted By: >>11194270

>>11189634
Ayyy lmao

Anonymous

Anonymous Mon 02 Dec 2019 12:18:25 No.11192931 Report

Quoted By: >>11193433

>>11192710
how is >>11191325 true if >>11191366 is false?

Anonymous

Anonymous Mon 02 Dec 2019 12:29:21 No.11192949 Report

Quoted By: >>11192955 >>11192972 >>11193355

>>11192758
you are kinda contradicting yourself, dude:

>We chose the nonnegative part because the real root function is also undefined for negative numbers

but also

>the symbols have a well-defined meaning
>That's a meaningless statement.

the $/sqrt{ }$ sign is well-defined. $/sqrt{ x }$ is the principal square root of x, and the principal square root of something is defined to be non-negative (it can't be negative, therefore it is unambiguous and therefore well-defined).

Anonymous

Anonymous Mon 02 Dec 2019 12:31:56 No.11192955 Report

Quoted By: >>11192972

>>11192949
>/sqrt
>/sqrtx
i meant ${sqrt{ }}$ and ${sqrt{ x }}$

Anonymous

Anonymous Mon 02 Dec 2019 12:37:46 No.11192972 Report

Quoted By:

>>11192949
>>11192955
now it's correct
>/sqrt
>/sqrtx
$\sqrt{}$
$\sqrt{x}$

Anonymous

Anonymous Mon 02 Dec 2019 17:21:31 No.11193355 Report

Quoted By: >>11193494

>>11192949
sqrt(x) for x element reals ist not the same as sqrt(x) for x element complexes. The latter is defined such that the principal values of sqrt(x) correspond to those that the real version would yield.
That's what I meant.

Anonymous

Anonymous Mon 02 Dec 2019 18:04:17 No.11193433 Report

Quoted By: >>11193454

>>11192931
I didn't say it's false, I said it doesn't make sense.
what do you think it means for one number to imply other number ?

Anonymous

Anonymous Mon 02 Dec 2019 18:24:46 No.11193454 Report

Quoted By:

>>11193433
yeah, true, my mistake. thought of the implication sign as of an equal sign for some stupid reason. >>11191325 is correct, >>11191366 doesn't make sense

Anonymous

Anonymous Mon 02 Dec 2019 18:26:55 No.11193458 Report

Quoted By:

>>11189634
this is pretty retarded ngl

Anonymous

Anonymous Mon 02 Dec 2019 18:28:27 No.11193461 Report

Quoted By: >>11193477

>>11191325
how is someone supposed to fall for sqrt(a) sqrt(a) /a is 1/sqrt(a)

Anonymous

Anonymous Mon 02 Dec 2019 18:38:48 No.11193477 Report

Quoted By:

>>11193461
nobody claims that

Anonymous

Anonymous Mon 02 Dec 2019 18:48:56 No.11193494 Report

Quoted By: >>11193497

>>11193355
ok. this is correct. $\sqrt{}$ is well-defined for real numbers, but not for complex numbers

Anonymous

Anonymous Mon 02 Dec 2019 18:51:09 No.11193497 Report

Quoted By: >>11193614

>>11193494
>but not for complex numbers
it is. it's the principal square root.

Anonymous

Anonymous Mon 02 Dec 2019 19:45:19 No.11193614 Report

Quoted By:

>>11193497
ok. i checked a little more, and $\sqrt{}$ indeed seems to be well-defined for both real and complex numbers.
why are there so many who don't know this? actually, i have never studied the complex numbers, therefore i'm not surprised that i'm so easily convinced about this. my original point was just that $\sqrt{}$ of something is defined to be non-negative (which is true, at least for real numbers)

Anonymous

Anonymous Mon 02 Dec 2019 22:10:11 No.11193966 Report

Quoted By: >>11194005

>>11191325
explain this shit. how did it go from (sqrt(a)sqrt(a))/a to 1/sqrt(a)?

Anonymous

Anonymous Mon 02 Dec 2019 22:24:12 No.11193998 Report

Quoted By: >>11194035

>>11189774
Yes, let's do things the way they were done before calculators were omnipresent.

None of my math or physics professors give two shits about it.

Anonymous

Anonymous Mon 02 Dec 2019 22:26:32 No.11194002 Report

Quoted By:

>>11191290
$<br />\sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right |<br />$

Anonymous

Anonymous Mon 02 Dec 2019 22:27:16 No.11194005 Report

Quoted By: >>11194042

>>11193966
it's just an implication sign, not an equal sign. the implication is from the equation on the left to the equation on the right, not just from (sqrt(a)sqrt(a))/a to 1/sqrt(a). actually, saying that a numerical expression (for example, (sqrt(a)sqrt(a))/a) implies another (for example, 1/sqrt(a)) is absurd. i made the same mistake at first lawl. here >>11191325 is just implied that, if $1 = \frac{\sqrt{a}\sqrt{a}}{a}$ , then 1 divided by $\sqrt{a}$ is $\frac{\sqrt{a}}{a}$ (because 1 equals (sqrt(a)sqrt(a))/a, as implied by the left equation)

Anonymous

Anonymous Mon 02 Dec 2019 22:32:12 No.11194018 Report

Quoted By:

>>11190898
That same reasoning could be used to say 2=-2, since 2^2=(-2)^2. Squaring is not a fully reversable function though, so it's not a useful or meaningful result.

Anonymous

Anonymous Mon 02 Dec 2019 22:37:40 No.11194035 Report

Quoted By:

>>11190234
>>11191261
exactly.
>>11193998
>he actually thinks rationalizing the denominator doesn't make it easier for a calculator
This is the type of shit that makes CS majors think they're smarter than us. You disgrace the field of mathematics.

Anonymous

Anonymous Mon 02 Dec 2019 22:40:29 No.11194042 Report

Quoted By:

>>11194005
Oh, I see now. Thanks for the explanation.

Anonymous

Anonymous Tue 03 Dec 2019 00:00:38 No.11194270 Report

Quoted By: >>11195264

>>11192921
nothing wrong here u incel

Anonymous

Anonymous Tue 03 Dec 2019 08:24:05 No.11195264 Report

Quoted By:

>>11194270
Who the fuck writes stuff like sqrt(x)*sqrt(x) = sqrt(x^2)
Just cancel the square root function at once since the power of x is the same value (2) as the square root

Anonymous

Anonymous Tue 03 Dec 2019 10:19:30 No.11195433 Report

Quoted By:

>>11190221
Not in this case, since $( \sqrt{2} )^2 = 2$ .
You need to make a consistent choice of branch of the square root function.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches