Take Any Square Root by Hand - Easy to Learn!

In just three easy steps, learn how to take the square root of any positive number, regardless of whether or not the result is rational!

The long division method is fast, efficient, and not too much different from dividing numbers normally.

If you have any questions, feel free to leave a comment and I'll get back to you as soon as possible!

[edwardbasdeo]

This method is really old . My primary school taught me this over sixty two years ago when I was preparing for Common Entrance Exam. Her name was Miss Valerie Retemeyer. God bless this dear lady

[EHeadhunterPL]

That was exactly the method I've been shown in school 35 years ago. I have forgotten the exact algorithm, and now that my daughter has asked me if it is possible to calculate a sqrt by hand, I am happy to share that with her. Thank you, sir!

[rogerhill]

I am approaching 80 and this is the first time someone has had the ability to explain it to me. Thank you!

[laytonjames]

I always remember this method as Horner’s method. Your description of the different stages is how I remember it, except that at each stage you double the number above the line, I.e ‘2’ becomes ‘4’ then ‘29’ becomes ‘58’ then ‘291’ becomes ‘582’ etc and then determine the red digit as you describe.

[nicholasragusano]

The last time I saw this was when I was in high school-1956 through 1959. We did it slightly different, with the writing of the numbers to the right of the system. We also left the square root sign in place instead of drawing a division box. We did need to remember to put a +/- in front of the answer, however. Thanks for the memories.

[aleks_ivanov]

Thank you, man. I cannot believe that the best explanation for this is coming from such a small channel. Keep up the good work.

[rontrail]

Great stuff, I've been a math nerd for a long time always happy to see things like this out there for the world to learn.

[rayseto]

brilliant! i remember learning a method of taking a square root from a book but never mastered that method, especially since I learned it on my own (they didn't teach taking square roots from all sorts of numbers, only the obvious ones). Thank you for making this video! Very clearly taught, too. :)

[sarkarsweet]

Most useful - I had learned this in school about eighty years ago, and later after learning the easier method of Log table-use did not have to use it! However, delighted to be reminded of this method again that should not be forgotten and remains useful for teaching youngsters that creates their interest in learning maths comfortably. - Ashit Sarkar (89 yrs young)

[reinymichel]

I used to teach this all the time in Ontario. Past the initial step, I used to say " Double the top, write it on the side leaving a space. Whatever fills that space must also go on top" Seems easier to do than your adding procedure for the side number.

[pietergeerkens]

I remember my Dad patiently, and carefully explaining this to me in Grade 3; while I sat in astonishment, shock and fascination thinking: "But I just wanted the square root of 25!"

I did remember the details well enough to put it all together some years later in high school, when my math skills were somewhat more mature.

Thank you for prompting a fond memory.

One point my Dad made was to place each digit of the result above the corresponding group that generated it; making placement of the decimal point quite obvious.

Love you Dad. Miss you every day.

[andrew_owens]

2 questions:
1) Who is credited with discovering this method?
2) Why does it work and where can I read about that?

[dennyoconnor]

I am the class of 1957 (yeah, that song) I was taught this by one Mr. Lynn Mauntner (amazed I remember his name). He also taught us logarithms, slide rule using a log log antilog slide rule (a four foot long one hanging on the wall) and after class he would show the few of us who hung around how to do things not in the syllabus for the class, like taking the cube root. I remembered (mostly) how to do the square roots and after you did the second step I was back in the rhythm (thanks) . Taking Cube roots I can sorta remember but I will need a bunch of hand holding (never used it after the precalculus course in 1956)

[stevenlitvintchouk]

I learned this method in elementary algebra class in junior high school. Most kids didn't have calculators back then, so the teacher taught us how to compute square roots with pencil and paper. But I totally forgot how to do it afterward. It was one of those things you learned to pass your exam and then dropped.

[trueriver]

Two details.

I would describe what you do as multiplying by the last digit.

I would also write the digits of the result over each GROUP. That way the decimal point automatically comes in the right place.

[raylucas]

Thank you. Very well done.
I am a retired QC mechanical inspector.
Always did my math with pencil and paper.

[bpark]

At 5:12 you get the 58. A much simpler way to get this is to DOUBLE the EXISTING answer gotten SO FAR. Double 29 = 58. Do the same at 6:41, doubling existing answer (29) to get 582. At 7:08, you talk about decimal point. This is much simpler if you write the answer digit over the last pair dripped down (spacing answer digits out). This way the decimal points will be vertically aligned. At 8:24 you double 2911 to get 5822. To illustrate the alignment, I show the final result calculations aligned as I suggest.
2 9 1. 1 4
4 8 47 65.23 47
4
58 4 47
4 41
582 6 65
5 81
5822 84 23
58 21
58228 26 02 47

[kazejah]

I'm 40, an engineer and part time math and science tutor, and since high school I've been pretty good with being to do everything mathematically by hand. And I've never learned this method lmao. Love it!

[brucelee]

I learned this method in my high school algebra class, in 1979.
This was the beginning of the era of hand held calculators.

One day, during class, I went to my teacher’s desk and asked, “Before we had calculators, how did people figure out the square roots of numbers?”
He showed me this same method.

All these years later, I have never forgotten it.

Thank you for sharing a video about this.

[BillDeWitt]

Thanks! I learned this in 5th grade (1960) from Mrs. Simms, but then forgot it. I looked around a couple of years ago and everyone on the internet wants to do a much more complicated and barely more accurate method. But this is more than adequate. Most of the time I want to use it is to estimate the Square root of a hypotenuse to the nearest unit value. Basically, "How much would we save if we cut across instead of going around?". Unlike the other methods, I can see doing this in your head.