Magical Squaring

Mathemagician Art Benjamin demonstrates and explains the mathematics underlying a mental arithmetic technique for quickly squaring numbers.

[@devvrattomar215]

Nobody is gifted out there It took his whole life to be of this level Salute to his HARD WORK

[@sauravsingh7271]

Devvrat Tomar Bro it is all vedic math.He has not developed that on his own.....

[@sauravsingh7271]

Devvrat Tomar they learn from us and then again teaches us back.

[@godkiller4020]

@@sauravsingh7271 but still for vedic math to work fast for higher numbers needs u to know other numbers square and addition to top that. I mean just look at his speed. And I doubt that if u learnt vedic maths they must have thought the derivation to u.

[@godkiller4020]

He is 50× or even more than my math sir who I know is very very smart. And ya I'm doing jee so u know who's teaching me.

[@ssn90]

@Reloaded Past The Iq tests are not very accurate in capturing intelligence... people have diff kinds of intelligence

[@MickeyMike100]

I am now squaring license plate numbers while walking the dog. :-)

[@tanmayjha7721]

Haha

[@ovrthmn]

Michel Lavergne, 😂😂😂😂😂

[@marbelc.barrameda1560]

witty man haha :)

[@angelopressley7689]

CTFU

[@punitsharma879]

hahahahah

[@Mr-Sudhanshu]

Never seen anyone explaining mathematics as simple as this.

[@Satya_Golu]

Ye Vedic maths hai kabhi Apne Sanatan dharma ke arth shastra ko bhi padh lo 1.एकाधिकेन पूर्वेण अर्थ: पूर्व वाले से एक अधिक प्रयोग: आवर्ती दशमलव भिन्न[recurring decimal fraction],वर्ग ज्ञात करने में,आंशिक भिन्नों द्वारा समाकलन[integration by using partial fractions]. उदाहरण: --वर्ग निकालने के लिए--(यहाँ केवल 5 से अंत होने वाली संख्याओं की बात की जा रही है)-- 25 का वर्ग:यहाँ पूर्व का अंक(संख्या) है 2 .----->2 का एकाधिक है 3. अब अंतिम हल है 2x3\25------->वर्गफल के दुसरे भाग में हमेशा 25 ही होगा. इस तरह 25 का वर्ग=625. 35 का वर्ग=3x4\25=1225, 175 का वर्ग=17x18\25=30625, 995 का वर्ग=99x100\25=990025.इत्यादि.

[@0h_f1ve85]

What did i just say...?

[@jab4634]

SIMPLE? 😲😨 I may be some time with this.

[@danquaylesitsspeltpotatoe8307]

you mean the david mitchell claymation thats bene left in the sun?

[@neilwayte579]

"If you can't explain it simply, you don't understand it well enough" ~ And this man explains it quite simply ~ Boo to my math teachers!

[@adityab.8715]

His confidence and happiness reflects his pure hardwork... Really enthusiastic teacher!

[@ksumar]

Plain genius. You have a very unique gift😊. I salute you Sir. Thank you for sharing. 👍

[@bhinbhinkaka6514]

@Diwana Kavi still you have to practice it

[@layshotterthanwasabi9560]

Diwana Kavi still it takes LOTS of practice. Let's say now we know how it works, then how long do you think you need to practice it to solve 8463 squared that fast?

[@sizlax]

@FACTS & knowledge He's still very well at articulating and explaining it. It really doesn't matter whom invented the method; if they don't have the platform or aren't able to explain it in a way that is easily conveyed and understood to the audience, then it is for nothing. This guy is a great proxy for the original work. Also, faulting this guy for teaching the methods in said book, is akin to badgering any other math teaching video for copying the teachings of the ancient Babylonians.

[@lordspongebobofhousesquare1616]

@Hitesh chourasiya maybe he discovered it on his own? It's not so hard to find out this "trick". Heck, I discovered this myself in high school. For a professor like him? Fnding this would've been a piece of cake

[@lekhapratap1652]

It’s called practice!

[@robertjones811]

"This is why it works" - at 8:00. A big thumbs up!

[@mannykhan7752]

Ive been watching this guy since the 80s when he hosted his Mathemagics tour shows. He is brilliant.

[@cabdurraxmanhassan5656]

All dislikes Are calculator manufacturers😂😂😂

[@OnlineStudyStation]

😂

[@tennisweekly2012]

And my teacher that says it’s not the better way to do it

[@Tech_Gamers]

Lololol

[@rajdwipdas5038]

Lol

[@ashadmemon1763]

😀

[@iliketheodds2575]

Impressive in that he can explain mathematically why it works. Kudos to you, sir!

[@TheRealPaul_Morphy]

For those of you watching this and thinking that you'll never bee able to do it it's because you need to improve your basic math skills first. You may have to practice 3 by 3 subtraction, 3 by 3 adding and 2 by 2 multiplication. Just time yourself on 20 problems in each subject and if you're around 1 to 2 minutes for the 20 problems you're ready to start learning this method for squaring.

[@rygeanpursues6965]

I' ll be practicing these from now on

[@IiIytIi]

You should take a look on his book, it's called Secrets of Mental Math.

[@danishkh4489]

Mastered it yet?

[@user-wd3sp7oy9l]

@@IiIytIi can u send link of his book

[@firstg4mer492]

after 3 years, are you able to square 5-digit number?

[@jakubszudrawski1324]

For those of you who would like the last problem in slow motion: 4913^2. He chooses 87. so now it is 5000x4826=5x4826x1000=(5x4800+5x26)x1000=(10x2400+10x13)x1000=(24000+130)x1000=(240130)x1000=24130000. Memorizes 130000=Dime. (Probably his mnemonic involves rules where 1 stands for nothing, 2 stands for something, 3 stands for dime etc. and then he combines them. So for example if it was 23000 it would be some other word plus Dime). Now he does 87x87=90x84+3^2=(9x84)x10+3^2=((9x80)+9x4)x10+3^2=(720+34)x10+3^2=(756)x10+3^2=7560+9=7569 now add that to 24000000+Dime (which is 130000)+7569=24137569

[@alial-khalili9232]

Wow

[@Quentijn]

Except for the slight typo (240130), perfectly summed up. Although I do think he went around 5000x4826 a different way: 5000x4826 means 4826/2 and add 0000 so 24130000. Feels easier and quicker.

[@cj-dd3qf]

the fuck u talkin bout

[@gautamvishwakarma3371]

9*4=36

[@SF-ki1sr]

Nice job! One slight correction. He said he was doubling 4826. As he referenced earlier with doing 51^2, he's dividing it by 2. So, he said doubling for 4826, he's dividing it by 2 to get 2413 (x 10) = 24,130... Keep the "dimes" is using peg system. d = 1, m = 3, s = 0.

[@MattiK2609]

I tried it with several three-digit numbers myself...and after only a few ones, I could do it using my calculator only to check the result!

[@usamiami6629]

+Matthias Köhler (MattK269) good job! try now practice with finance questions in Finmath app itunes.apple.com/us/app/finmath-financial-mathematics/id1085429075 i hit just Associate level

[@oh_dat_guy4740]

Ikr same I just found it so fascinating and it was so fun for ms

[@oh_dat_guy4740]

Ikr same I just found it so fascinating and it was so fun for me

[@saravananrajaram6791]

Matti2609 jmdukh

[@rajeshjha9215]

It is indian vedic math that is taught to whole world

[@ST0ICSAGE]

Do you guys have to brag this in each comment, have some fucking shame dude

[@Samgon95]

Your brain is Amazing sir...

[@user-jm6gp2qc8x]

😂😂😂

[@hellsowner8513]

hol- up

[@rdjs18]

This video deserves a million likes.. Hats off to this genius 👏

[@jamilAhmed-vs9oj]

Hello

[@RahulKumar-ry9jy]

Hii

[@curiouscollectiblesAU]

If it was published under a channel named Arthur Benjamin it probably would have. If MAA could show they have possession of this guy’s prowess then the million are earned.

[@soulreaper1306]

@@3acreations So , he applied that not like you Indians who never respect Veds and Vedic Maths , now when others are using it you are getting jealous . Ya , he should mention that , but it will be of more use if he teach them that , as knowledge is important more than its source . If you had respected your Vedas , then India would have been developed more than others . you sing of Ancient Glory . But don't understand that what you are now matters , not what you were. Most of you , I mean don't even believe them , thatswhy Vedic Maths books are found lying in trash which is one of least selling books. P.S. I don't hate India or you , I just meant to say that come out of your bubble as no one gives a damn about your past . Only what you are now matters , which I called the hub of wasteful students supporting terrorists and politicians too backing them like hell .While criticising your government for even trying to get into NSO or bring uniformity in your country . That's the impression I got of your country .

[@lukes2219]

Pallavi Shukla I’m assuming he didn’t invent this but idk

[@FIFAisFizz]

Mathematics has always been my favorite subject and it's you sir, who made me go crazy for Mathematics... Love from India ❤ I'm sure that I'm gonna meet you in 2025... You are my best teacher...

[@rounakrai8187]

yo same dude ~rounak

[@spongebobsucks12]

You mean year 45^2 ... right?

[@TheSeventhTraveller]

@@spongebobsucks12 😂 Bro, you made my day

[@bryantryy7100]

You sir just taught me something no teacher ever could. I literally just successfully found the square route of 76 and checked it to be correct. My cat was jumped as I shouted YESSSS! haha

[@vedprakashpandey4119]

There is no magic though. This is simply (a)^2-(b)^2 = (a - b)( a+ b). Adding b^2 both sides: a^2=(a-b)(a+b)+b^2. Anyways, this video is very helpful. I appreciate him for putting this up.

[@evccrtt1480]

Ved Prakash Yes we all know the formula But not many thought about its application

[@peterkappiah5861]

what kind human are you? you are too amazing. i want to be like you.........

[@thegame6822]

He's not a human bro he's a GOD at Math

[@devayushkar1317]

absolutely correct

[@Akhiljnao]

Be like u don't become a Xerox copy

[@btdpro752]

Just practice

[@btdpro752]

His a human, either put in the effort or stop saying you want to be him

[@samirubhatt]

I used to be a teacher and i just loved the way this was explained. In simpke words without rushing and gets into head so so easily.

[@artiehess7110]

When this guy was a student at Mayfield High School (Ohio), he was brought into my 8th grade algebra class at Mayfield Middle School (1978-79 school year) and taught the class his methods for squaring numbers, and I still use them today.

[@johanmusic2263]

Your love of mathematics is inspiring! Thank You.

[@BushCampingTools]

Professor Benjamin has improved my mathematics so much LOL. I wish I knew how to do it this way 50 years ago LOL but now my son benefits from this! Fantastic and I just subbed!

[@codemathlab]

he's a genius. he is really amazing. I have never seen anybody in my life doing this sort of stuff. oh! he's a true genius.

[@thomasdahl3083]

You can save time by memorizing all the squares from 10 to 100 to begin with. Since you already know how to square numbers ending in 0 and 5, there are only 70 left to memorize. So it is not that impossible if you think about it. In less than a week you should have it done. To calculate addition faster you can visualize that you read the numbers from a whiteboard, you see the numbers there, just like when you see them written with your eyes open. I think that's why he closes his eyes while doing the addition in his mind. But you also need to learn how to do subtraction quickly in your mind, for the first step when you go down. 71 to 100 -> you see easily that it is 29, but the other way: 71 - 29 is not that fast unless you have learnt how to do that quickly in your mind. And the arm and body movements help him increase the brain's speed to jump to the next step and the next step and so on. Our human brain likes to take pauses, but you must force it to continue with the calculations, step by step, there is no need to freeze the thought on a specific result when you have more steps to do. I think this is the hardest part to master.

[@elorm294]

I used to think mathematics had no application until I met him. Thanks so much for sharing

[@RyanTheHero3]

I look at the thumbnail once at this is what instantly goes through my mind: *‘Nobody should be that happy when they hear maths’*

[@shivamtrivedi1684]

This is what you call a you tube recommendation 😎. We should admit that we didn't get this , we searched this .

[@ishigamiyu1991]

Been 5 years and 364 days and this video is still amazing

[@birdmomentos5953]

The information you hold is as gold to humanity...

[@Progresser436]

Thank you sir for sharing your knowledge with us, and thank you for simplifying math. 😀👍👏

[@moedbz]

I wonder why there are dislikes

[@awawpogi3036]

UMPESH because they are fucking trolls

[@RatedRudy]

jealousy

[@sedeanimugamez5418]

They feel bad about their low iq

[@soulreaper1306]

Jealous stuff on internet

[@Wrench-007]

Gym teachers

[@shiwanshtiwadi3590]

Very nicely explained Even a layman can understand Wow man

[@user-co3ev1xu4h]

You sir litterally blew my mind.

[@adasiddiqui128]

you made things much easier to understand. thanks

[@yuzhenwang8103]

Even with this method, I can't compete with a calculator, Amazing human brain!

[@rajdeepbisht413]

Try vedic mathematics book bro buy it from amazon

[@rehaanmahmood4568]

Practice

[@anymaths]

watch my maths videos to do calculation easy.

[@Satya_Golu]

It's Vedic math brother 🇮🇳 1.एकाधिकेन पूर्वेण अर्थ: पूर्व वाले से एक अधिक प्रयोग: आवर्ती दशमलव भिन्न[recurring decimal fraction],वर्ग ज्ञात करने में,आंशिक भिन्नों द्वारा समाकलन[integration by using partial fractions]. उदाहरण: --वर्ग निकालने के लिए--(यहाँ केवल 5 से अंत होने वाली संख्याओं की बात की जा रही है)-- 25 का वर्ग:यहाँ पूर्व का अंक(संख्या) है 2 .----->2 का एकाधिक है 3. अब अंतिम हल है 2x3\25------->वर्गफल के दुसरे भाग में हमेशा 25 ही होगा. इस तरह 25 का वर्ग=625. 35 का वर्ग=3x4\25=1225, 175 का वर्ग=17x18\25=30625, 995 का वर्ग=99x100\25=990025.इत्यादि.

[@impossibleaimswithinfinitc3904]

Thanks for donating you precious knowledge

[@preetioswal6652]

First time a math vid is awesome. Loved it

[@ivanv23hr]

Thanks to this guy i will more easily squaring 2 digit number in my head ☺😊. For 3 digit numbers and up i need more experience

[@giraffe7632]

that is a unique gift

[@victorgustavo4366]

In Brazil i'm not learned this tricks in my school. God bless this man.

[@beebeejoo]

Spectacular teacher and will be really helpful for dealing with numbers in daily life.

[@MohaMMaDiN55]

You are an amazing professor. Hopefully I can find a video of you teaching us how we can find the root of numbers without using calculators. I’m also looking for tricks for division problems.

[@robertarmstrong3024]

In "The Great Courses", which can be ordered online, he gives 24 one hour lectures, and in one he does exactly what you asked.

[@EdTheUndeadHead]

That moment when you're looking for ASMR and actually learn something really helpful

[@yashrajtiwari3115]

This is the best , fastest and easiest meathod ever . I salute you. Ad can never thank you enough.

[@aakashrathour2592]

You teach how actually mathematics works. Excellent sir.

[@Purebeautyluv]

He is so adorable. I definitely learned something new!

[@nishabansal8828]

Sir l am also a mathematician. YOU ARE MY INSPIRATION

[@domthebomb4878]

I wish I had a good teacher like this

[@arshthakur9172]

A simple yet brilliant trick! 👏

[@shwetatiwari2381]

Amazing method

[@chalopadhtehai2706]

Unique person! Thanks sir

[@johnbaptist8193]

Indeed, you are a number wizard. This video is very informative. I have tried up to 4 digits okay; but I couldn't come out as fast you you do! It's God'd gift to you. It's great that you are sharing to others; it is really good.

[@jobairulislam3910]

Really enjoyed the full classes.. 💜

[@muqikhan5593]

you are a genius i surprised my teacher like when she called me dumb.. and she asked me square of 19 and we get 361 and everyone clapped but then she asked 99 and I answered after couple of seconds 9801 and I gained my respect 😎

[@brijeshverma3432]

In my country India.. The tricks shown here is taught to a student of 8th standard..And it is so simple...

[@kamalmadani2846]

well in Belgium we do these methods too but in 4th grade, everyone can do it, its only the speed that is extraordinary . He's soo good god bless him

[@vaibhavrao8485]

Aaaaee both of you don't lie....I live in India it's false and I visited Belgium and it's false

[@happychoudhary328]

Love you sir !! Awesome concept with short tricks

[@dhruvvraghu6226]

I spent a few months pondering about it and no joke i kind of figured it out on my own.. But there was always something missing.. Your video brought my memories backs RN explains where i went. wrong.. Thank you for sharing this

[@prathamkumar5224]

Don't tell me I am the only one who knows he is doing Vedic maths Still a very good explanation

[@1prahladdas]

this is vedic math only

[@fictional6734]

Correct

[@MathVidushi]

@@fictional6734 Yep - check this out kzbin.info/aero/PLIV1J7y0QOo9tWfzvq6-CFR4w0ND0-uBU

[@bubalumalu4928]

The way he speaks about his work is so interesting

[@joelgrayson4648]

I love this trick. Thank you so much!

[@balajikkl7956]

Would long for to live the rest of the days in my life with the people like you...

[@joppadoni]

i worked out that x^2 + y^2 +2xy= the square of any number. if the number is (xy)^2. hence 51^2 is 50^2 + 1^2 + 2*50*1. This works equally for every number. So a 3 digit number can be expressed as 124^2= 120 ^2+4^2 +2*120*4 Although id never get to it as fast as this practitioner, and wonderful educator x. however there must be a formula for 3 digits, 4 digits as well.. just never worked it out yet..

[@joppadoni]

also worked out that 3 digit numbers are worked out by x^2 +Y^2 +Z^2 + 2 ( XZ+XY+YZ).. interesting series. Unlike baseball, which is just rounders

[@yogeshwarnath4869]

What did you work out this is the too old method of squaring

[@abdoulainyang7098]

You must have been the professor of the mathamatical association of America bcus u are a genius.

[@yogeshwarnath4869]

@@joppadoni mr. Joppadoni These formulas werre discovered by our maths teachers hundreads year ago

[@whereswaldo1376]

Wouldn't the x^2 + y^2 +2xy method defeat the purpose of squaring any complicated number more than 100? I mean, you still have to square a 3 digit number to find the square of another 3 digit number. Like, to find 124^2 you have to do 120^2. Also that method is pretty simple because it's basically the regular (x+y)^2 formula.

[@ktenergy1202]

Thanks I tried traveling d with any number and brought it back with A and it still works I now I know how algebra works

[@paulstanlev459]

Thanks for your this Valuable Gold gift Sir. God Bless You Fore ever and ever...

[@viralmyst1427]

Damn, people like you that spread your knowledge to others are one of the greatest kinds of people

[@nikoszervo]

Easy right? How can someone be able to do this 3-steps in his mind in 1 second lol! He is amazing!!!

[@bimanh.saikia6600]

I like this man...he is awesome..

[@lakshyatyagi9924]

Excellent sir, really excellent. KZbin is a nice platform to learn just because of awesome teachers like you.

[@deltaexplorer47]

WOW !! AMAZING !! Thank You professor.

[@IR240474]

Thank you so much for this...!!! My stats teacher is going to piss herself when I can complete half of a one-way anova by the mind alone!! hehe....Now to find the video on how to multiply 2 digit numbers like 24 x 39 etc...

[@That_One_Guy...]

easy , you just need to scatter those number into the nearest easy number : 24 = 20 + 4 , 39 = 40 - 1 thus 24 x 39 = (20+4)(40-1)

[@IR240474]

Thank You!!

[@That_One_Guy...]

you're welcome :)

[@smallgift540]

24 x 39= 30 x 24+ 9 x 24 =936 :)

[@elviopapa5251]

start from left to right, we have 2 x 3 (20 x 30) so we have 600 record the 600 in your head and continue, 2 x 9 (180) add to 600 is 780 and add 3 x 4 (120) 780 + 120 = 900 ok still have the 900 in your head and add 4 x 9, 936. this is the answer, the method is multiply straight, cross, straight, I X I. so if we have 43 x 67 we start with 4 x 6 = 2400. and we add 4 x7 = 280 we have 2680 and we add 3 x 6 is 180 so 2680 + 180 is 2860 + 3 x 7 = 2881

[@shubhamsrivastava3641]

Love from India. Genius

[@hazemswelam5716]

My teachers have been trying to teach me how to square numbers for years now, but I just learned it in just 12 mins. This dude is so cool

[@manishchandwani5575]

I always thought I'm best at mathematics and then I saw you. I'm no where near you, I know about tricks and all but doing it that quick in mind is something I won't be able to do. Respect sir 🙏

[@nikettiwari3168]

How do he calculating too much in mind ???just amazing men.

[@NoobPatel]

Genius guy! However, this video called me dumb in so many ways 🤦‍♂️

[@Satya_Golu]

It's Vedic math brother 🇮🇳 1.एकाधिकेन पूर्वेण अर्थ: पूर्व वाले से एक अधिक प्रयोग: आवर्ती दशमलव भिन्न[recurring decimal fraction],वर्ग ज्ञात करने में,आंशिक भिन्नों द्वारा समाकलन[integration by using partial fractions]. उदाहरण: --वर्ग निकालने के लिए--(यहाँ केवल 5 से अंत होने वाली संख्याओं की बात की जा रही है)-- 25 का वर्ग:यहाँ पूर्व का अंक(संख्या) है 2 .----->2 का एकाधिक है 3. अब अंतिम हल है 2x3\25------->वर्गफल के दुसरे भाग में हमेशा 25 ही होगा. इस तरह 25 का वर्ग=625. 35 का वर्ग=3x4\25=1225, 175 का वर्ग=17x18\25=30625, 995 का वर्ग=99x100\25=990025.इत्यादि.

[@superbatsamanpradhan7638]

Teaching style is superb ....Perfect teacher

[@pravakarvardhan3010]

I am from India. You are great sir.. This is the best explanation ever

[@sanjeevkant8470]

You are a rockstar

[@enjoi971]

good job!

[@adityaabhishek1598]

He is the real mathematical genius... wish we would have these types of teachers in our future

[@MuhammadYusuf-ni3cn]

I enjoyed and learned. These are the most important thing of this video.

[@anymaths]

watch my maths tricks to learn something.

[@shadowguy6029]

awsm the trick is just mindblowing

[@briankerr4098]

Holy Crap ! I've been doing math in my head this way without even knowing I was doing it this way ! Maybe I'm a math genius & didn't even know it ....

[@moblegamming4658]

Same I dont concentrate either I remember back in first grade my teacher used to teach like take 1 in your finger and 6 in your mind and shit which I did not use to calculate I used my brain

[@moblegamming4658]

The teacher used to give us a whole page of simple maths as HW in first grade and I hated HW so I did it in the class itself with my friends i calculated so fast that after i finished my friends had completed 2 columns out of 10

[@GianniTuratta]

We can generalize the equation at 8:30 to multiply two arbitrary integers A and B. Notice that (A+d)(B-d) = AB-dA+dB-d^2 = AB - d(A-B+d), hence AB = (A+d)(B-d) + d(A-B+d), and notice that if A=B we retrieve the eq. at 8:30. For example consider: 26*33. The nearest easy number is 30, so subtract 3 from 33 and add 3 to 26: 29*30. Then add 3*(26-33+3) = 3*(-4), so: 26*33 = 29*30 - 3*4 = 870-12 = 858.

[@ikosecarltonekoli3256]

Thank you Benjamin. I'm Carlton, secondary school maths teacher in Cameroon. God bless you for me

[@rizwanabegum4473]

Awesome... Now i can show off by squaring numbers faster than a calculator 😂😂

[@Faraz_sfh]

Good techniques shared. It will help the youngsters to learn more about the maths.

[@Snowflake_tv]

Amazing. I love it. It makes me compute by heart more faster than before.

[@nishantviradiya6935]

You are not common person...you are unique..... brilliant .. awesome

[@nitishkumarsharma3251]

sir I'm from India you are great sir

[@bob7644]

Smart asllllll. Damn boy I’m bouta look like a genius in math class

[@quantumshepherd5532]

Wow! I'm inspired! Way to go Art Benjamin!

[@memoona6397]

OMG!!!!!! You are a REAL CALCULATOR. A BIOCALCULATOR!!!!!!!!!! GENIUS!!!! Not everyone is as fast as you are. I wish I had a Maths teacher like you. Keep it up.

[@balikakamble1433]

awesoe. thank you so much sir.

[@anujkumar7289]

Hi

[@evan.5967]

1:48 if you look close enough her battery is on 69%

[@justsomeguy892]

nice

[@evan.5967]

@@justsomeguy892 yummy

[@macdonald1032]

I really enjoyed your lesson .

[@martingsilva]

Thank you Sr. I do appreciate it! Thanks and good luck!