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From: Davidson1956
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  • Thank u i need this for my icse board exam thanks a lot long live you thaaaaaaannnnnnkkkkkkssssssss a lotttttttt

  • Very good. You explained that far better than the horrible math teach I had in high school.

  • @6:54 your explain how an irrational (square root) must continue is really clever and elementary and makes the case for teaching the algorithm justified - because you get two ideas for one. (Of course, your mini lectures are really all about 'proof', and its centrality to mathematics, aren't they.)

  • Thank you! This is coming up in a test about trigonometric functions and I'm going to need this to calculate the length of the hypotenusa of a straight angled triangle. I have a good feeling about this.

  • thanks a lot!

  • I tried it against 7, but it was not working. You're not clear that the first time you subtract, you're not subtracting 1 from three, you're subtracting 1 squared from three. Once you do that, it works: you get the nearest whole square like long division, but because you're moving squares, you have to square each decimal point (2 working digits for every answer digit) to get the correct square remainder.

  • oh thank you sir!!!!!! i thought i would never be able to know it.. it will be comming in my exam and you tought me.. THANK YOU!!!

  • i got it ...well taught..... Yor teaching was fantaatic

  • @UnholyMaulz Thats because he's not saying questions

  • We were never taught this in Ukraine. It wasn't until I immigrated to England with my Father that I learned math similar to this, but I had never seen this. Thank you, @Davidson1956. I'm currently studying for a test, this will come in handy. ;D!

  • Wait WOah...Grade Nine????  I'm using this to solve equations in my 8th grade physical science class

  • thanks this is a cool pattern

  • u rock sirji

  • @xCombatArmsHackx If you're still having trouble, try this method on this video. It should be more what your looking for, "Simplifying Square Roots in 60 Seconds"

  • Thank you so much for this! I have to write a program that square roots any given number in MIPS and i couldn't figure out how to get a more precise result by using the method:

    B = (A+(X/A))/2, C= (B+(X/B))/2, D=(C+(X\C))/2 etc....

    X is the number chosen to be square rooted, and A is an arbitrarily chosen number that is less than X. It works, it's just in mips, It's just I'm having trouble with the result being more precise. Thank you!

  • @xCombatArmsHackx Just realize how bad education sucks now days. Step up your game bro.

  • Awww, no story? I'm slightly disappointed.

    Interesting stuff.

  • i started by watching funny videos and then went to music then i some how came here?? weird

  • I'm in grade five and I figured it out.It's easy.

  • this really helped!!!

  • im sad that i never did have to learn this in school :(

  • I'm in 7th grade, and i am learning this in school

  • NEEEERD! :)

  • You confuse me!!!!

  • thanx a lot

  • @xCombatArmsHackx dude i totally agree

  • Thanks!!!!

    This helped a lot! :)

  • welcome to the MI6 now double the 7 @ 3 57

  • thanks soooo much this helped me big time!!!!

  • Comment removed

  • But do it without the decimals then and put them in later 20578. It will probably be like 140 but then you know 14 is the answer.

  • ok well i get that sort of, but how would you solve like 205.78. you can make it a pair because the decimal is in the middle

  • What did he say in 3:58 to 4:00 i didnt hear it clearly in the video anyone please tell me

  • thankyouuuuuuu! this helped me so much :)

  • Thank you very much,.. it'll help big time in my exam tomo :)

  • Most impressive. Sucks to be the generations that doesn't know this stuff because the last generation screwed up education. Wish I had know that one in school. It would have helped.

  • WOW! Thanks a lot man!

  • Thank You! I have a very important test for a very important job tommorow. The test is essentially all algerbra,complex algabra, and no calculators are allowed, i actually never solved a square root with out a calculator [I mean its 2011 not the primitave big bang era (joke), who doesnt use a calculator]anyways, you helped, thanks

  • Comment removed

  • Is there some way to prove why this process is correct?

  • There is a way; I worked it out a couple years ago.  It involved a lot of algebra and was very tedious. If I can ever figure out how to get back on Davidson1956 I may do a video on it.

  • @SSCCMath142 I suppose that the double zeros have something to do with 3 being the square of the result and the fact that we use zeros is because of our base-10 numerical system. But I cannot speculate further. :(

  • this is my maths question which i dont know how to do please reply: THERE IS A METHOD TO WORK OUT THE SQUARE ROOT OF A NUMBER WITHOUT USING A CALCULATOR. DEMONSTRATE THIS MEHOD BY FINDING THE SQUARE ROOT OF 108241 USING A MATHEMATICAL METHOD . DO NOT USE A CALCULTOR , GUESSING OR TIAL AND ERROR METHODS . CLEARY DEMONSTRATE THIS METHOD :)

    please someone helpppppppp

  • The same method outlined in the video works on any number. Start with splitting this number up into pairs of digits: 10 82 41, then follow very similar steps.

  • @SSCCMath142 omg pleasseee this is due tomorrow can u please tell me how to do it like stepp 1 . step 2 . step 3 etc ay can u state it cleary using the number 108241 becoz i cant hear him if u cant dw , its not that im lazy its becoz i just moved in and we have no speakers please reply ASAP

  • I'm sorry, but i'm very busy today, and I doubt I could write it out here anyway. Your message was not very clear because the English was so bad, but I got that you don't have speakers with which to hear me. Let me suggest getting a cheap set of earphones, or watching this at a local library if you can.

    Good luck, hope you make it!

  • I'll have to keep on practicing that

  • What is the Square root of Nuts?

  • YES!!! I PASSES MY TEST THANKS!

  • ok i had 2 wait like 1 minutes + to get the method  THANK U SO MUCH I DONT CARE IF I HAD 2 HEAR UR STORY IS KINDA INTERSTING ILL COME BACK 2MOROW TO COMMENT IF I PASSES MY FINALS!!!

  • @milexmexicana99 this is my maths question which i dont know how to do please reply: THERE IS A METHOD TO WORK OUT THE SQUARE ROOT OF A NUMBER WITHOUT USING A CALCULATOR. DEMONSTRATE THIS MEHOD BY FINDING THE SQUARE ROOT OF 108241 USING A MATHEMATICAL METHOD . DO NOT USE A CALCULTOR , GUESSING OR TIAL AND ERROR METHODS . CLEARY DEMONSTRATE THIS METHOD :)

    please someone helpppppppp

  • @POSTALIFE i did passed my finals i acctually understood dis method more than wat teachers r teaaching dis days cuz all kids r teach 2day is da fast way 2 do it8(

    i got an 84 on my test 4 me thats like wow! usually i got like 70 or 60 even 50s! da teacher couldnt belive it she though i was cheating but i was like nope i acctually studied n she was like IM SO PROUD!

  • great method but that is too many steps, b/c i have to spend 1.30 minutes per question.

  • Comment removed

  • @mackles Why show the world how childish you are? Why not simply click on another video? stupid people scare me!

  • @mackles - If you had to ask the question, what is a square root, and ask it in that manner, then you are not ready yet for the definition, go back about 30 lessons and start over

  • Why do old people alwas say the name of the year? " I learned it back in 68"

  • I will never understand this.

  • im guessing your david's son whom was born in 1956, am i right or am i right? i'm right.

  • why are all these videos from 08!?

  • Because that's when I did these videos! And yes, my last name is Davidson.

  • thanx alot it helped me very very much..... pls upload a video for cube roots

  • good stuff

  • thank you very much coz that question came in my xam

  • rrrrrrrrgh I keep doing 5, but I keep getting the wrong answer :(

  • Thank you very much, it helped me a lot! :)

  • Hey this is nice . thank you !

  • oh no math is my weakness

  • Now the numbers can interfere with one another so it may be necessary to revise your guess. I don't have much success posting links but anyone interested can Google "square root by hand" and it's the first hit.

    Towards the bottom there's a detailed explanation of the cube root algorithm.

  • I'm hogging your response area, but two things: I committed a pretty heinous abuse of notation in my last post. In x(2+x)<2, maximum x is .7 but when I multiplied both sides by 100 then x would be 7. I shouldn't have used the same variable.

    Also, the method for cube roots is similar but, as you would guess, takes more work. For example, after the first step in finding the cube root of 34 you end up with something like x[x(90+x)+2700]<7000.

    (continued)

  • This can be written as x(2+x)<2, where 10x is an integer by considering place value. Multiply both sides by 100 to clear decimals to get x(20+x)<200. This is the step of dividing 200 by 27. Basically it all comes down to the fact that (a+b)^2=a^2+2ab+b^2, and this is where the multiplication by 2 comes in.

    Also, like the division algorithm, you get the error at any point. Look at the numbers you subtract. 1.73^2=1+1.89+.1029=2.9929, already pretty close. Very clever.

  • Thanks for the clear demonstration. I had never seen this method before but I like it. I don't think the explanation is too difficult, actually the idea is the same as the one behind the long division algorithm ie successive approximations.

    After the first correct digit of 1, we know that (1+x)^2=3 for some x we try to approximate next. Expand to get 1+2x+x^2=3. Now we want to find the largest x that gives an answer less than 3 (much like long division).

    (continued)

  • what´s the answer?

  • @arnez1973 im watching it cause i wna u cant stop me

  • Stupid teacher...

    I asked my math teacher how to calculate square root back in 6th grade, and she told me there was no method, and you needed a calculator to get it.

    I will never trust teachers anymore.

  • @TheFlyingTiger129

    oh that is sad that your teacher said you needed a calculator. when i was a kid in math, calculators were about 1,000 dollars to buy. and forbidden in class. you would be expelled if you brought one. not that you could afford one. i learned the above method, but this video is confusing me. probably because i am getting senile. i was shocked to find that now calculators are required in math classes. might be why cashiers at stores can no longer count back change. no joke.

  • @northbeachfilms

    Math has advanced in such a way that formulas become too complex or tedious to perform without machines. We're not talking about fractions or algebra here, so please rethink what you say before you pass a judgment on the new generations. Not all of us are lazy and lack a work ethic. Remember, think smarter, not harder.

  • @ElnAlter mentioning the difference between classrooms in the past & today does not mean that i think people are 'lazy and lack a work ethic.' i said calculators were 1.000 dollars & considered cheating. and noted that today they are required. a straight observation. you are projecting some issue you have that is unrelated to my post. it is true that cashiers do not know how to count change back & very possibly a byproduct of calculator use in class. however, that is how evolution functions.

  • My respects to you as a student and as an observer.

  • i just gonna use a calculator

  • quite a good method

  • this is youtube not a school i like to be free of grammer spelling etc on the internet

  • @MegaTheWatcher well why the hell are you watching it then.

  • @MegaTheWatcher  STFU

  • Holy crap, I get it! :D Thank you so much.

  • wow im in 7th grade and this is easy to me .. u people r stupid

  • Dear Mega The Watcher, Thanks for the comment, and I'm glad you got it. Just a little friendly advice. Don't be so quick to criticize, because math doesn't come as easily to some, and yet they may be smart in other ways. And please learn to write in good English or people may unfairly think you are stupid! Jon Davidson, author of this video

  • @SSCCMath142 you said "learn to write good in English"

  • because he doesn't explain it like a great teacher like me could do... jejejeje

  • i am sooo confused!

  • thumbs up if this guy talks too much in the beginning

  • If you really want to get this technique, it's like learning anything else in math: You'll do better by writing each step down (and pausing the video) and trying to understand that step before moving on to the next. But if you have a specific point you're still not getting, please point it out.

    Why it works is a whole 'nother matter. I figured it out a couple years ago and the algebra is very tedious and large, but it is entirely algebra. Maybe I'll video it sometime. (Davidson1956)

  • Is this because you didn't understand some of the steps or because you'd like to understand why it works?

  • Thanks! You helped a lot!

  • why put a 7??

  • @231AKazak because 27 x 7 = 189, which is as close to 200 as he can get without going over. If he did 26 x 6, it would be low and 28 x 8 would be too high. You see it's kind of like fractions where you have to do to the top what you do to the bottom, but in this case you have to multiply by what you do to the blank space. So if you had 2_ and you made it 24 you would have to multiply by that 4. 24 x 4.

    It's really hard to explain.

  • This is one thing that Chuck Norris couldn't do!

  • @Undertakernd Chuck Norris does this in 2 seconds

  • @Undertakernd because his too busy playing with calculus.. that finishes ur sentence lol

  • you have to go throughn this for a square root of 3 OMG!!!

  • @MARVELAG

    no, it can be done much faster in ones head.

  • Great vid!

    I looked up how to find a cube root and it very similar to the method you taught in this video. All you do differently is have groups of three 0's and a couple of other minor changes.

  • math without a electric calculator... i would fail math

  • Thanks you totally helped me with my homework. I am 7th grade Algebra 1 so I need a lot of help, thanks.

  • Thanks you totally helped me with my homework. I am 7th grade Algebra 1 so i need a lot of help, thanks.

  • Thanks you totally helped me with my homework.

  • Thank you very much for this video! I had forgotten this and was struggling to teach my kid! This is very helpful. We both sat and watched your video and now we are good. You have explained it very well. Thank you. You have very good teaching skills. Hopefully you can upload more such middle school and high school math videos.

  • i did the same with number 4 :D

  • Thanks Sir. It waz very informative...

  • Hahahaha! Is to easy

  • Very well presented, thanks!

  • thanx ....this really worked

  • Hello sir, thanks for the help. It is easy to follow and effective. Now I can share to my students this technique. Thanks. Godspeed.

  • You save my grades!

  • Ah, nevermind. I found the problem. I assumed that since you got 1 for the first quotient and then subtracted 3 by 1, that you simply subtract it by the first quotient.

    You actually have to square the quotient of the first number and subtract it from the first number. My bad.

    I think you need to be a bit clearer on that first step, though. It might be why cars2024 also can't find the solution for the square roof of 7.

  • Comment removed

  • This system doesn't seem to work for the square root of 7. Once you get to the step of getting to 4_ multiplied by _ = 500, you'll find there is no number below 10 that can be added to the blank to create 500.

    Either I did something wrong, or there's a different process for numbers once they get to a certain level.

    Either way, could you explain what to do when in a situation like this?

  • why do you have the same method that somebody else on youtube already used

  • wow thannx very much sir it worked really well!!

  • my number is 520000 its easy with a calculator but how do u do it with hand ?

  • My head is broken!!

  • Awesome teacher!!

  • im not getting it

  • if you are doing 3√ do you then insteadof haveing 2x0 behind the . you put 3 0

    (3. 000 000 000)? and tripple the number instead of the double?

  • can you please show the prove or why this method works?

  • I'll consider it, but it's a very messy proof with lots of algebra. I figured it out a couple years ago and I'm not sure it would lend itself well to YouTube audiences. But I'm glad you're interested.

  • @DavidsonSSCC thanks I am going to have to teach a friend how to do this. Years ago in calculus 3 I stumbled upon a really easy way to find any root but I've forgotten how I did it! I still have my class notes I think I'm going to try and rediscover that really easy way. I think I just made a little F(x) and found the diveritive. Or something like that. thanks again.

  • What you're thinking of is called Newton's Method. It's a very efficient way to find a square root, or any root for that matter. For example, if you want to solve for the fifth root of 7, use Newton's to solve x^5 - 7 = 0. It uses a method called a fixed point iteration to converge to the desired root of an equation, and yes, there's a derivative involved.

    I may do a video on this when I get a chance.

  • Excellent ! Thank you.

  • thats perfectly simple thanx for showing us the formula thats the right way to find the exact number

    as well as the easiest way

  • this is still an estimation method... it's cool but (for ex.) the "27" part is pure guessing..

  • thank you, great video xD

  • Excellent explanation. Very very useful. Thankyou so much for your time.

  • plz tell me the largest perfect square numer and wat that means . im taking an ACT tomorrow so if some one can plz hlp me because im 12 years old and i want to do good on it.I would be happy if any one can hlp me !THNX!

  • A perfect square number is the square of an integer. For example, 4, 9 and 25 are perfect squares, being 2 time 2, 3 times 3, etc. There can be no largest perfect square since there are infinitely many integers to square!

    Your message was almost unreadable.  Please do yourself a favor and get in the habit of writing in good English. Someday it will pay off.

    Good luck on the ACT!

  • Thank you,I already took the ACT and i only answered half of the questions on there because I'm 12. But next time i will know wat to expect and thanks for the info. i wasn't on the test BUT NOW I CAN IMPRESS MY MATHEMATICS TEACHER

  • you mean you want to do "well" on it. -proper english-

  • Wow all of that is going on inside my calculator when i tap a couple of buttons? That was extremely useful

  • I suspect that it is much more complicated than that in your calculator! Calculators, like all computers, work in base 2 numbers inside instead of our base 10 numbers. There are other ways to calculate square roots. My guess is that calculators use logarithms. Such calculations would resemble very long polynomials with 0's and 1's in place of the variable.

  • Thank you very much,Professor Davison......loved it!!!

  • I'm sorry why is a number being double after the first square root? ie 1 double to 2 as well as why 7 is place behind the 2? I'm purely asking in understanding logically, not the problem of just solving because i can do that with a calculator.

  • well its, like long division. Its a series of steps that mathematicians figured out to give u the answer. I completely understand ur question because i myself like understanding, logically, why we do "that" thing in the step. I figured out the why's in long division, but for this method, i have no idea.

  • THANKS SO MUCH

  • I tried to figure out cube roots but they seem messy. This is how far I got: you divide the number into groups to the left and right of the decimal point just like for the square root, except divide into groups of three digits each. Then at each stage you seek the next digit X such that (gasp!) (300*Y^2 + 30*Y*X + X^2)*X is less than the current running difference (Y is the cube-root-so-far). So instead of the nice (10*(2*Y) + X)*X (the square root case) we have this monster. How to refactor it?

  • Great try! I'm very busy with the beginning of winter quarter at my college, but I hope to look at this in the next week or so when things calm down. I know there is a method for cube roots and that it's very non-trivial, but I'd rather figure it out like you have tried than to track it down in some other source.

  • You lost me at 3:44. I understand that you doubled 7, which equals to 14, but with the 3, I have no idea what you just said, and how you got 3?

  • Thank you sir for helping me to find out the square roots without calculator. If i have any mathematical doubts, i would reach you. Thank you so much.!  - Vinodh , India.

  • nice lesson. to complement your lesson on solving odd number, check my video on solving perfect squares. 5 stars to you!

  • this helps a lot ,thank you!

  • sorry but you lost me at 2:17

  • Can you help me with 2 digit numbers of square rooting?

  • Thanks, The teachers never told me this :)

  • in the first step, do you use the units digit or do you use the whole number?thx im am 12

  • THIS WAS SO HELPFUL!!!

    THANK YOU SO MUCH!!!

    I have an exam day after and i wasn't getting how to do this but now i do!!!!!

    THX so much..

    I will keep referring this video in the future also :)

  • tHanKS siR>>>>^^

  • thanks you so much!

  • DUDE YOU ARE AWESOME!

    My maths teacher explained this in class but i didn't understand him AT ALL.

    Thanks sooo much!

    5 stars+sub

  • extremly helpful

  • Comment removed

  • That was pretty helpful.

  • thats sweet it so cool

  • u r smart. : )

  • in Romania, this is the only method for finding a square root's decimals that is taught in schools. we use a different layout, but technically it's the same.

  • good to hear that in some countries one is still taught to use his head rather than the calculator. respect!

  • Thank you for showing you method.

  • I have used the Babylonian method as well as a Slide Rule to calculate square roots without an electronic calculator.

    Your method appears to reach the correct answer faster than the Babylonian method, which requires an initial guess and some averaging. The Slide Rule approach is limited by the user's visual perception of an imaginary number line (depending on the size of the slide rule and user's age), which results in limited decimal place precision.

    Is your derivation an original?

  • this is cool lol

  • Can you make a video showing another example? I tried out your method but it works correctly until the square root of 8. When i tried to find the square root of 8, it got to a point where i would have to put a 10 where there is supposed to only have one digit (when it got to 564_ , i had to put 10 on that blank) and i don;t know what to do in order to compensate for it. It's hard to explain but you'll get my point if you try it..

    THANK YOU!!

  • yes cube root's can be done like that, it's almost the same process but there's a couple more steps involved. Maybe I'll get in a little more practice and post a video.

  • Thank you. I last calculated square roots by hand around 40 years ago, and I'm happy to refresh my brain cells.