In general, it will be difficult to compute the square root of a decimal number manually? Examples : 50.73 71.21 156.45
I need to calculate the SQRT of  $x$ to $y$ decimal places. I'm dealing with $128$-bit precision, giving a limit of $28$ decimal places. Obviously, if $\,y &gt; 28$, the , which I'm currently using, becomes futile, as it simply doesn't offer $y$ decimal places.  My question to you is, can I calculate the Square Root digit-by-digit? For example, calculating the $n$-th digit, assuming I already have digit $\,n - 1$. I'm well aware this may be impossible, as I've not found any such method through Google yet, just checking here before I give up in search of arbitrary precision methods.
How can I prevent iTunes from auto starting when I plug in an iOS device? Is one time pad cipher reuse and random key secure? Homeomorphism between the unit disc and the unit square I know that the function that describes the homeomorphism is: $f(x,y) =       \begin{cases}     \frac{x^{2}+y^{2}}{\max(|x|,|y|)}(x,y) &amp;\quad\text{if } (x,y)\ne  (0,0) \\       \text{} (0,0) &amp;\quad\text{if } (x,y) =  (0,0) \\       \end{cases}$  But it's impossible to me to show that $f(x,y)$ is an homeomorphism. Mostly i can't see the injectivity. Using contracted forms ("don't", "let's") in a formal text How compelled should I feel to use non-contracted forms (do not rather than don't and so on) when writing in a rather formal text, say an academic paper? In one case I am afraid to seem too stilted, in the other, too casual. Are there good guidelines?  And are there differences in this regard between British and American English?  (In this  there was not much more than "Contractions are more frequent in informal than formal contexts".) Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$ Is there any utility to check whether my laptop battery is in healthy condition or not? Is there any utility available on Ubuntu to check whether laptop battery is in healthy condition or not? Is using only HTTPS bad in a SEO perspective? I would like to set up a new business site. I plan to direct www.example.com to example.com and only use that domain. My plan is also to only use HTTPS and not HTTP.   Does this affect the SEO for the site? E.g. do Google put lower or higher rank for sites that is only available via HTTPS? What is strain? Why does DNA coil upon itself? I have been reading Lehninger's Principles of Biochemistry to understand DNA supercoiling (pg-). Supercoiling is the twisting of a DNA upon itself and this happens when the two helically wound strands of DNA are either underwound or overwound. The book says that this act of underwinding or overwinding generates a structural strain  which is then accommodated by coiling of the DNA upon itself (supercoiling). Here the word strain has been used in the way stress of mechanical physics would be used. I wonder if it means stress. Besides I would like to know how underwinding or overwinding cause the DNA to coil upon itself. Excerpts from the book:  DNA supercoiling is generally a manifestation of structural strain. Most DNA are negatively supercoiled (which means that the supercoiling is left handed). In almost every instance, the strain is a result of underwinding of DNA double helix. Supercoiling is not a random process; the path of the supercoiling is largely prescribed by the torsional strain imparted to the DNA....  Torsional strain, again is it talking about ? P.S. The description of the question has been changed recently. Give a one-to-one and onto function from $\mathbb{N} \times \mathbb{N}$ to $\mathbb{N}$ Is there an expression to indicate the strategy of wearing someone down with numerous small irritations? I would use rope-a-dope, but it's got connotations of pretending to lose that I don't need. I'm trying to describe the behavior of someone who sends twenty detailed emails a day about various projects, and the recipient of his emails has finally gotten tired of trying to parse them, so the recipient just agrees to whatever he proposes. I'd like an expression that evokes both outward earnestness and hidden creepiness, like Uriah Heep, Dickens's "Humble servant" with veiled ambition, who overdoes it with professions of humility until he's in power. Water torture would work, but comes too close to a more racist expression that I'm not comfortable with. On the recent changes to flagging and limits Looks like flagging has been affected by releases today. Are these intended effects?   Higher daily limits (appear doubled for me, flagging of posts limit also doubled).  Explained by Shog9 below. Soft comment deletion  - e.g. for "accept rate" obsolete comments - it does in fact work, but the immediate feedback is gone.  This is fixed now. Has the throttling rate changed?  Seems possible to repeated flag without waiting 5 seconds.  If it was broken, it isn't anymore. Old soft deletions that were neither categorised as "helpful" or "declined" have all become "helpful".   If limits have been updated, can we get the new formula published? Not changed, as confirmed by Shog9. Why did the Resistance automatically assume the use of this tech in The Last Jedi? Adjoint pairs, triplets and quadruplets Often we have adjoint pairs $(A, B)$ (meaning $A$ is left adjoint to $B$). Sometimes we have adjoint triplets $(A,B,C)$ (meaning $A$ is left adjoint to $B$ and $B$ is left adjoint to $C$. No adjoint relation between $A$ and $C$ obviously, since they have the same source and target).  So the first question is: can we have quadruplets $(A,B,C,D)$ ? (meaning that $C$ is also left adjoint to $D$).  Second question: It would be then possible that we have $(A,D)$ besides $(A,B)$. But I think not, because I think that it is not possible to have a functor $A$ with two different right adjoints, $B$ and $D$. Is this correct? why is the set of all binary sequences not countable? Variable wavelength IR Diode? I was thinking of building a DIY IR Spectroscope but for this, I need to find an IR diode that can do variable wavelengths. So far I have looked at Farnell and Mouser but all the diodes I have looked at seem to be fixed on a wavelength.   Is this possible? or would I need some sort of filters and optical equipment, if so which parts would I need?  Thanks. The new Top-Bar does not show reputation changes from Area 51. Definite article, repetition in lists Which would be correct?        The fridge, the shelves, the walls, the floor, and John himself, were all covered in foam.   The fridge, shelves, walls, floor, and John himself, were all covered in foam.      The the can be applied to all the nouns, so is there a need to repeat it? How can I get a new browser session when opening a new tab or window on Firefox/Chrome? When opening new Internet Explorer window, a new browser session is issued. Therefore you can login with two different accounts on the same service (let's say ). The same does not apply when opening a new tab in the same window in Internet&nbsp;Explorer.  How can I get a new browser session when opening a new tab or window on Firefox?  How about Google Chrome? “Unable to Connect to World” Minecraft PE 1.16.201 So my brother and I have been playing Minecraft together on our iPads for years now, but in September I got a new iPad Pro 3rd Generation and I’ve been having issues with Minecraft ever since. Every time we have tried to join each other’s worlds we get the message “Unable to connect to world”. Recently after the update on December 16th, it worked for about a week without having any issues, but now it has gone back to not letting us connect to the worlds. Both of us are able to connect to other people’s worlds, but not each other’s, we’ve tried many things to fix this but so far nothing has worked. If you have any ideas for what we should do please let me know, thank you so much! What is the earliest work considered to be Science Fiction?