I have proven that the sum of any two irrational numbers is not always irrational and that a rational plus an irrational is irrational, however I am not sure how to prove this specific case.  I was thinking along the lines of: $\sqrt{2}+\sqrt{3}=n$   where $n$ is an element of rationals. By squaring both sides  $$(\sqrt{2}+\sqrt{3})^2 = n^2$$ $$7 + 2\sqrt{2}\sqrt{3} = n^2$$ I have proven the sum of a rational and irrational is irrational yet it is too long and complicated to prove that root two and root three make root six. Moreover, it will be an additionally difficult to prove that two times root six is irrational so I was wondering if there was a quicker less complex way to finish this proof?
Can the expression $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m \in \mathbb{N}$ are perfect squares? It doesn't seem likely, the only way that could happen is if for example $\sqrt{m} = a-\sqrt{n}, \ \ a \in \mathbb{Q}$, which I don't think is possible, but how to show it?
How to recover a deleted NTFS partition with data Let $D \subset \mathbb{C}$ be the open unit disk, $f:D \to \mathbb{C}$ a holomorphic function and $d=\sup \{|f(z)-f(w)|:z,w\in D \}$. How can I show that $|f'(0)|\leq \frac{d}{2}$?  I tried using Schwarz's lemma on the function $g:D \to \mathbb{C}$ defined by $g(z)=\frac{f(z)-f(0)}{d}$, but I am only getting $|f'(0)|\leq d$. How do I make my own horse follow me? I've found a horse in Skryim and I ride it a bit to explore the wild but when I dismount, it wanders away and doesn't stay where I leave it. How do I stop it from doing this? Is there a special thing I forgot about horses? I didn't steal this horse - it was from an Imperial Fort that I've cleared. $n\in N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $\lim\limits_{n\to\infty} a_n\cdot n = 1$. $n\in N,   a_{n+1} = a_n  (1 - a_n)$ , $0 &lt; a_0 &lt; 1$. Prove that $\lim\limits_{n\to\infty} a_n\cdot n = 1$. I proved that $\lim\limits_{n\to\infty} a_n = 0$ and that $a_n$ is strictly decreasing. I tried Cezaro Stolz but didn't get anywhere. Thanks in advance. What are the meaning and possible origin of "word!" and "word up"? Why is my document pdf generated by pdflatex looks different from the one generated by latex+dvips+ps2pdf ? From the code below, i have tow different papers switch to the tow cited commands above :  \documentclass[10pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[francais]{babel} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \usepackage{lipsum} \author{M ROUAN SERIK} \title{Article with \LaTeXe} \fontfamily{cmr} \begin{document} \maketitle \section{Titled section} \lipsum \end{document}   Here's my pdffonts for the tow pdfs : Pdflatex:    name                   type     encoding  emb sub uni object ID   ------------------------------- ---------------- --- --- --- ---------   AMTRHA+SFRM1728        Type 1    Custom   yes yes no       4  0   DPTCLU+SFRM1200        Type 1    Custom   yes yes no       5  0   JVZRKA+CMMI12          Type 1    Builtin  yes yes no       6  0   UEWNID+SFBX1440        Type 1    Custom   yes yes no       7  0   FOVERL+SFRM1000        Type 1    Custom   yes yes no       8  0     latex+dvips+ps2pdf      name                                 type              encoding         emb sub uni object ID   ------------------------------------ ----------------- ---------------- --- --- --- ---------   WVMUEH+SFRM1000                      Type 1C           WinAnsi          yes yes no        16  0   ZHRBNN+SFBX1440                      Type 1C           WinAnsi          yes yes no      14  0   IMJWCD+CMMI12                        Type 1C           Custom           yes yes no      12  0   MDMSVR+SFRM1200                      Type 1C           WinAnsi          yes yes no      10  0   TWHNMT+SFRM1728                      Type 1C           WinAnsi          yes yes no       8  0 I only get four video output options Even when I start a brand new file in Blender, I only get four video output file options: AVI raw, AVI JPEG, Frame Server, FFMpeg Video.  I am running version 2.78.5 (I'm using the beta so that I can use denoising.  How can I get access to all the other video outputs other people have? Like this: Check if email exist php How can I change GNOME Shell theme? How do I update Custom Label's value using apex? Which one would be a better option metadata api or tooling api? Please provide example I'am working on post deployment automation process in salesforce. I am stuck on how should I update values in custom labels which needs tobe updated manually after a sandbox refresh. Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true? Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?    It seems to me like they are equal definitions in a way.    Can you give me a counter-example?    Thanks How do I bake multiple texture maps into 1 UV, In Blender Cycles? Does measurement, quantum in particular, always increase the total entropy? How does SO's new auto-login feature work? SO and SU just told me I've been logged in. I'm guessing because I'm already logged into my Google account... but how does SO know that? Man/Tree Symbiosis It was an old book... I'm pretty sure it was a book, and pre-1990's I think. The basic plot was this man somehow interacted with this tree, and as a result he became a carrier of the tree's 'seed'. They were in a symbiotic relationship: the man got a much longer life, more strength, etc.; but when he did die the tree would grow up from his body. Fantasy book where a young prince becomes a mage When I was younger (11-12 years old, so the early 2000s) I once read a story where a young boy, who may have been either a young prince or a squire of some sort, is recruited by a wizard and taken to a city to train as a mage.  I seem to remember him living in dorms with the other children at this school, until he gets into difficulty with another of the boys in the dorm. He is kicked out of the dorms and ends up living above a blacksmith shop (I think).  I remember it being the first book in a series of books of which there were about 3 out at the time. I think one of the stories was about the boy going to a tower to do something or other.  Does anyone have any idea what this book series is? I haven't been able to find it for years now but it was a story I really loved. Countinuity of the identity map between different topologies Moving one object causes other to move another (already tried unlinking) Do indexes work with "IN" clause Do spice containers need to be hermetic? Spice containers purchase  I'm planning on upgrading my spice storage. Reading some advice online (e.g. , and ) I came to the conclusion that spice containers should:   Not be exposed to direct sunlight and high temperatures Be airtight   Which means that either you store it inside of some closed cupboard/wardrobe/room or you have containers which do block light and are in a relatively shady place. And the containers need to be airtight.  Available solutions  I've been browsing for some containers available online in my country and the 2 most sensible options I've seen are these:       The problem  The first one is hermetic (it has some rubber around the lid) but it's clear glass. The other one does not have the rubber, just a regular twist-off lid, but it's amber glass.  It'll be hard for me to find any space inside of cupboards to store all of my spices (I need at least 30), so I'd rather buy amber glass container, which I believe will effectively block the sunlight, even when kept on the counter. But I can't find any hermetic amber-glass containers, only ones with regular lid.  The question  Is that regular twist-off lid enough to keep spices airtight and fresh? Or should I focus on buying a hermetic container (like the one in clear glass). I could then for example paint them black to block the sunlight.