Find the value of $\dfrac{\sqrt2 + \sqrt6}{\sqrt{2 + \sqrt3}}$.  My book is showing that this problem has an exact integer value solutions, but I was unable to find it.  How can we prove that it has integer solutions, and which integer is its solution?
Find the value of:$$\frac{\sqrt{45} + \sqrt{18}} {\sqrt{7+2\sqrt{10}}}$$      I need help solving this question. Every reply is appreciated.  Thanks!
Is there any way to script Windows 10's "color filter" feature programmatically? Given two date ranges, what is the simplest or most efficient way to determine whether the two date ranges overlap?  As an example, suppose we have ranges denoted by DateTime variables StartDate1 to EndDate1 and StartDate2 to EndDate2. How can I make a script (or make some changes) to allow me to turn the screen off in Ubuntu (12.04) whenever I want, the way thevscreen can be turned off in Cellphones?  And how can I make a combination of keys (a shortcut) to execute that script?  I want to conserve power.  I've seen this question    but there is no hotkey for it.  Moreover, in the answer, it is said that there are many ways to accomplish this so I'd like to know more. What is the best way to determine the number of days in a month with JavaScript? I've been using this function but I'd like to know what's the most efficient and accurate way to get it.  function daysInMonth(iMonth, iYear) {    return 32 - new Date(iYear, iMonth, 32).getDate(); } This is what is supposedly his claim:     My noumenal self is an uncaused cause outside of time, which therefore   is not subject to the deterministic laws of nature in accordance with   which our understanding constructs experience.   How can he say that if a noumenal self has to exist in nature and be bound to body that exists in nature? Also, if his noumenal self is free then so does 7 billion other people's, which is not the case because they all live in a societal structure where everyone has freedom that comes with a bunch conditions as to what is forbidden. Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $ In Avengers: Infinity War, up until Thanos      gets all six Stones   in order to use the Gauntlet he needs to close his fist, as we see in the fight scene on Titan.     Doctor Strange: "Don't let him close his fist!"   So why later does snapping work? What is the point of the `cd` external command? Suppose that I have a group $G$ of order $p^{2}q$ for two distinct primes $p$ and $q$.  I need to first show that one of its Sylow subgroups is normal.  I start by letting $H$ be a Sylow $p$-subgroup and $K$ be a Sylow $q$-subgroup.  If $K$ is not normal, then letting $r$ denote the number of Sylow $q$-subgroups, I have that $r|p^{2}$ and $r\equiv 1$(mod $q$).  I also have by the second Sylow theorem that $r\neq 1$.  So $r = p$ or $p^{2}$.  If $r = p^{2}$, I can write out the Sylow $q$-subgroups, and count their combined elements to show that $H$ is uniquely determined and then again imply Sylow number $2$ to obtain that $H$ is normal.  But if $r = p$, then I cannot see how to proceed.  Can anyone give any advice?  Thank you.  ( I am happy to provide more detail for the $r = p^{2}$ case if it is desired or appropriate. ) I want create my own IDE but I want a code editor that would syntax highlighting.  I want to embed it as a control into a WPF window.  Malcolm The usual Schrodinger Lagrangian is $$ \tag 1 i(\psi^{*}\partial_{t}\psi ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi, $$ which gives the correct equations of motion, with conjugate momentum for $\psi^{*}$ vanishing. This Lagrangian density is not real but differs from a real Lagrangian density  $$ \tag 2 \frac{i}{2}(\psi^{*}\partial_{t}\psi -\psi \partial_{t}\psi^{*} ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi $$ by a total derivative.  My trouble is that these two lagrangian densities lead to different conjugate momenta and hence when setting equal time commutation relations, I am getting different results (a factor of 2 is causing the problem). I can rescale the fields but then my Hamiltonian also changes. Then applying Heisenberg equation of motion, I don't get the operator Schrodinger equation.   Is it possible to work with the real Lagrangian density and somehow get the correct commutation relations? I would have expected two Lagrangians differing by total derivative terms to give identical commutation relations (since canonical transformations preserve them). But perhaps I am making some very simple error. Unless all conjugate momenta are equivalent for two Lagrangians differing by total derivatives, how does one choose the correct one?   I guess the same thing happens for other first order systems like Dirac Lagrangian also. Is there a way to copy maintenance plans from one SQL Server 2012 to another? Both servers are not accessible via the same copy of Management Studio at the same time (on different networks). How do I add a launcher for .sh applications? I have installed ubuntu (11.04).  I installed phpstorm which is simply an archive for you to extract and shove in your /opt directory.  To run it you would use /opt/PhpStorm-103.243/bin/PhpStorm.sh  In unity I had created a launcher on my desktop.  Now I have installed gnome-3(gnome-shell),  And I have nothing in my desktop.  So how do I run phpstorm quickly? Can I get it to show up in "applications"? What should I look for when buying a used bicycle? I'm moving to a city where I can ride a bicycle to the grocery store, coffee shop etc. I want to purchase a decent used bicycle. I'm leaning towards a bike that's in between a "10-speed" or road-bike and a mountain bike. What should I look for when choosing a particular bike?  I've never purchased a used bicycle. Other than classifieds (e.g., Craigslist), what types of places can I look? What other issues should I consider, such as size, visual appearance, leaking tires, etc.? How can I make sure it's not stolen? Why must a field whose a group of units is cyclic be finite? Let $F$ be a field and $F^\times$ be its group of units. If $F^\times$ is cyclic, then show that $F$ is finite.  I'm a bit stuck. I know that I can represent $F^\times = \langle u \rangle$ for some $u \in F^\times$ and that we must have that $|F^\times| = o(u)$, where $o(u)$ denotes the order of $u$ in $F^\times$.  I tried assuming $o(u) = \infty$, but I'm not sure exactly where to go from there. I was wondering if I could get a hint. I added two torus objects, and when I click one of them, it also selects the other. They both share the same node thing. I want to delete one of them, but it keeps on deleting the other with it. I can't even undo placing the second torus without removing the other. I'm trying to use itemize inside a tabularx environment, but I have a problem when I mention the end of the line. It seems that using \\ end the line after the end of itemize, resulting in a supplementary vertical spacing that I would like to remove.  Any hint?  \begin{frame} \frametitle{Sujet de thèse}         \begin{center}             \textit{Sujet N$^\circ$221 : Formation et dynamique des champs de dunes longitudinales.}         \end{center}          \begin{tabularx}{\textwidth}{l !{\color{blue}\vline width 3pt} X}             Contexte &amp;  \scriptsize{Classification des dunes selon leur mécanisme de croissance, leur orientation et leur forme.              Bonne compréhension :             \begin{itemize}[noitemsep,topsep=0pt, label=\textbullet]                 \item du mécanisme de croissance lié à une disponibilité en sédiment grande.                 \item de la croissance sous un vent unidirectionnel.             \end{itemize}} \\             Objectifs &amp; \scriptsize{Etude de l'orientation longitudinale :             \begin{itemize}[noitemsep,topsep=0pt, label=\textbullet, parsep=0pt ]                 \setlength\itemsep{0cm}                 \item Développement d'un formalisme sous des vents multidirectionnels.                 \item Etude des dunes longitudinales dans le cas d'une faible disponibilité en sédiment. (Fingering mode)                 \item Inversion: données topographiques $\longrightarrow$ Données de vents $\rightarrow$ paléo-climats.              \end{itemize}} \\             Outils &amp; \scriptsize{Modèle numérique (Rescal), Données expérimentales, Théorie.} \\         \end{tabularx}     \end{frame}     And yes, dunno if it's important but everything is inside beamer. As you know, we can enable the spell checker on single line text boxes in the following way:    We have to enable it every time for checking words.  How can we enable it forever, so it doesn't need to be enabled each time? How precisely do I need to post close to 7:00 (somewhere) to get hero of time? Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$