How to find the square root of 2 using simple algebraic rules

Ever wondered how to discover the value of the square root of 2 using simple algebraic rules?

I’ve been through plenty of maths books and 99.9% of them haven’t demonstrated how this feat can be accomplished.

Today I’m going to share with you the methods which you can use to find the value of irrational numbers as continued fractions, and in the process you will learn how to write the value of the square root of 2 as a continued fraction.

See the mathematics below…

{ x }^{ 2 }=2\\ \\ { x }^{ 2 }+x=2+x\\ \\ x\left( x+1 \right) =\left( x+1 \right) +1\\ \\ \frac { x\left( x+1 \right)  }{ \left( x+1 \right)  } =\frac { \left( x+1 \right)  }{ \left( x+1 \right)  } +\frac { 1 }{ \left( x+1 \right)  } \\ \\ x=1+\frac { 1 }{ x+1 } \\ \\ x=1+\frac { 1 }{ \left( 1+\frac { 1 }{ x+1 }  \right) +1 }

\\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ x+1 }  } \\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ \left( 1+\frac { 1 }{ x+1 }  \right) +1 }  } \\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ x+1 }  }  } \\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ \left( 1+\frac { 1 }{ x+1 }  \right) +1 }  }  } \\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ x+1 }  }  }  } \\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ \left( 1+\frac { 1 }{ x+1 }  \right) +1 }  }  }  }

\\ \\ x=1+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ 2+... }  }  }  } \\ \\ x=\sqrt { 2 } \\ \\ \therefore \quad \sqrt { 2 } =1+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{ 2+... }  }  }  }

How To Add Latex Formulas, Equations and Expressions To Your Maths Answers On (For Google Chrome Users Only)

Let me guess… For the past few days you’ve been on but for some bizarre reason, or due to your own laziness, you just haven’t been able to add Latex formulas, equations and expressions to your beloved answers. Whilst your fellow friends or foes were seamlessly copying and pasting Latex codes into their answers, it turned out you were calling yourself the most hideous names in front of your computer screen. You eventually became so upset with yourself that you decided to do something about the lack of “Brainliest” answers and praises you were receiving – hence the reason why you’ve landed on this pathetic page. Yes, I’m calling this page pathetic because after all it was produced by a loser like me who had nothing to do in his spare time. Think about it, who in the right frame of mind would spend hours answering maths questions on a “homework help” site?

Ok, so now that I’ve offended you – you probably want to leave this page, however, please remember why you got here in the first place. You simply want to add Latex formulas, equations and expressions to your answers so that you can pick up extra “Brainliest” answers and have’s users massaging your ego. Since it most likely is the case, bear with me for one moment and let me explain how you can perform such a feat with a minimum amount of fuss…

Now, I’m assuming you are a Google Chrome user because this post has been written for “Google Chrome Users Only”. If you aren’t a Google Chrome user – then surely you like the sound of my voice, or more specifically my average writing skills – and for that I’ll praise you. It’s not often people spend seconds reading my posts let alone minutes or hours.

Oh, you’re still here? I guess you are a Google Chrome user after all, therefore I’ll hurry up and demonstrate how to add damn Latex code to answers.

You’re probably familiar with the “Chrome Web Store”. If you aren’t, here’s its link: . Now, what you must do when in this store is search for the app “Daum Equation Editor” because this app is spectacular and in a league of its own (the guys who developed this app haven’t paid me to say this). This app will let you produce mathematical formulas, equations and expressions in Latex and copy and paste them into your answer boxes on Furthermore, you won’t have to produce any Latex code whatsoever to achieve your lifelong ambitions. Life can’t get any better than that can it? …Copying then placing mathematical codes in to answer boxes on

Assuming you have downloaded this app thanks to this post,  play around with it and explore its degrees of freedom. If the expressions you have produced are satisfying, then copy and paste the relevant Latex code it provides you with (underneath your expressions) in to your beloved answer(s) on Make sure it sits within the [tex]…[/tex] tags which can be produced by clicking on the “paste/edit equation” button that can be found on answer boxes on Brainly’s site.

If you have any questions concerning copying and pasting Latex codes in to your answer boxes, just message me on my profile page or comment on this post.

Bye, bye for now. Have fun answering maths questions. Hehe. 🙂

Video Updates: 01.07.2015

This week’s updates are as follows:

You can learn how to draw a tesseract using the video below. This depiction of a tesseract can be found in the book ‘The Visual Guide To Extra Dimensions (Volume 1) – Visualizing the Fourth Dimension, Higher Dimensional Polytopes and Curved Hypersurfaces’ written by Chris McMullen Ph.D, a particle physicist based in the United States.

This next video contains a few perspective drawings and an animation of a sphere passing through a sheet of paper. It was made to demonstrate that perhaps the universe we inhabit is a construct of some kind.

You can explore non-euclidean space, or more specifically – a 3 dimensional sphere with lines passing through it both vertically and horizontally…

For those interested in seeing basic shapes rotate, you can watch a line, square and cube rotate about 360 degrees and additionally; a point, circle and sphere spin around an axis below…

Now, most of these videos were made in order to help me visualise a few concepts brought to light in Chris McMullen’s book. I hope you do get to enjoy watching these new clips. Feedback is appreciated as always. 🙂

Maths Videos For Web News…

This month I managed to upload more proofs to my Google “A Level Maths Proofs” page which can be accessed through this link []

I also made a few new maths videos unrelated to proofs for those interested in mathematical art and funky ideas. I must admit, the quality of my videos (in terms of their resolution) weren’t that great, but hopefully you’ll like them.

My latest clip is called “Percentage Count (0% – 100%)“, designed for those who are struggling to understand what percentages really are. This video illustrates that one percent of something is really one part out of a hundred  equal parts of an object. You require one hundred hundredths to produce 100% which is quite simply 1.00.

Free A Level Mathematics Proofs


Today you can download and view my hand written A Level maths proofs. These hand written proofs can be found at:

If you do decide to share my work, please make sure my web links remain intact so that I can continue to build and re-invest in

As always, I strive to produce the clearest A Level maths proofs on the internet, so that you can pass your C1, C2, C3 and C4 exams with flying colours. I’m not the kind of tutor who simply tells students to plug numbers into formulas. I make sure my students understand the problems they’re dealing with – using proofs and logical models.

Thankyou for your attention. 🙂

GCSE + A Level Mathematics Proofs, Videos and Tutorials.