Square ANY number up to 1000 in 5 seconds - math trick!
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- Опубліковано 28 чер 2024
- Square any number up to 1000 with this easy to understand fast math trick!
How fast? Some can be done instantly - others will take up to 5 seconds - as you can see in the thumbnail.
For this math technique you will square each of the digits then add them to the digits multiplied by themselves and 2...all really easy calculations.
This trick is based in Vedic math - an Indian system of mathematics.
Maths is made easy with tecmath helping!
To donate to the tecmath channel:paypal.me/tecmath
To support tecmath on Patreon: / tecmath
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#fastmathtricks
#mentalmath
#mathtrick
I love how excited and proud he sounds.
Why does the comment says '10 years ago' '3 days ago' wait wha-
Wait what
@@lfn4p829 It's... his name
@@lfn4p829 I wrote the comment 10 years ago, and edited 3 days ago.
@@BenDreemurr44 lol , I love your sarcasm
I am a math teacher from Egypt, and I and my pupils benefited from your methods of explaining mathematics and I would like to thank you a lot
You should trade your job with him. 😬
اجدع ناس
I already did that.
@@mytravls :|
تحيا مصر و المدرسين المصريين. 🇸🇦❤️🇪🇬
It took me a solid three minutes to realise that this is basically (a+b)^2 = a^2 + 2ab + b^2. A very creative way (and yet simple) of applying this.
wow wouldn't of picked this up :)
:OOO didnt even realise
Yeah ikr, I love how people say "they dojt teach this in the schools" where they have been taught about this since 6th grade itself. Took me only a few seconds, when he said "twice the number"
no it isnt
@@scottcaine4514 yes it is
He sounds like he's always on the verge of laughing
🤣
😭😭😭
no cap lol
💀💀💀
Wow this fact made me laugh
Imagine this guy is your math teacher how much better would this be .
True
Textbooks and homework is what students had prior or before podcasting was available. The results reflect the difference in performance by the students!.
😂🔥
Not at all. School system has a different purpose which is to teach you the concepts. Whereas, these shortcuts which are a distilled form of those concepts serve a different purpose, which is to make your calculations faster. Both have their place.
No.
It’s ridiculous how much this channel improved my mental math in so little time
Pls solve 798² bro
I didn't get it.
@@tudor__ but how dude
@@unpluggedalphaa
792^2
498164
12744
112
636804
quite easy but i know what you might have done wrong, you wrote 126144 instead of 12744 right?
@@KGR_ 😀 thank you brotha
Didn't realize the thing i needed in life was an Aussie man showing satisfying math hacks
dat choice of words.
Very useful video, This method would have never crossed my mind in a million years and I would have been stuck doing it the hard way in my finals, But now I'm armed with an easy and surprisingly fun method. Thank you a lot
I am 70 years old and grew up loving math and doing math games and quizzes with my father. I miss math class. These problems had me smiling and getting them right...”Come on! Give us another one!” 😊 Thanks! BTW, I’m in South Carolina, USA
got me by 11 years LOL but I was doing the same sitting here in Tianjin in China at 4 am LOL
@@hellow1444 How is that an unreasonable age?
@@hellow1444 why?
Lack of reply from Amy might imply she indeed Was 70
@Ed EdwardsThat’s apart of the American dialect. It is not a typo
This man sounds like he’s on the verge of yawning when speaking
for me it feels likes he's on the verge of laughing out loud
Most accurate observation ever...
Now I'm yawning when I hear him speak. 🤭
For me it sounds like he´s about to giggle all of the time
You consistently blow my mind mate. Mathematics is such a beautiful subject and I find this so appealing. Thank you for all you do
Not only can you extend this to any number of digits, but the 3rd power stuff, while not likely something you can work out manually, is very interesting. It basically adds another thing to multiply in each of the steps: the number you are trying to square with various digits 0'd out. Unique to 3rd powers. For example, say you wanted to calculate 84345458^3 using this method. The second step in the other method has you multiply digits 1 and 3, 8*3 here. Then you need to multiply that by 80345458 and then finally multiply all that by 3, instead of 2. The 0's in the number are always the digit/digits you skip over in each step. This 80345458 number is completely absent in 2nd powers.
You truly have a gift for teaching and numbers... A very rare combo mate!! 👍
Thanks mate
@@tecmath 👍
That's not a gift,that's simply (a+b)^2
@@arwen3478 you use (a+b+c)^2 lmao whats wrong
@@karenamma7716 you wont be able to tell that if this video havent told you about this in the first place lul
Hi Josh. Just wanted to say a big thanks for your vids. My son and I love the clear, simple explanations that make maths so much easier. 👍. Matt
I love your positivity, it makes it so much more fun to learn math concepts!
Thank you so much for breaking this down gently and positively. I love mental math and your channel is really fun.
You are the Mister Rogers of math, Josh! Thank you for your gracious style and clear instruction. It is a genuine pleasure to listen to your lessons. I have learned so much from you. I have suffered for decades with math anxiety to the point of mental paralysis. Thanks to your teaching vids, I'm doing math in my head quickly and accurately. I appreciate the many new ways of thinking about numbers and mathematical operations that you bring to the table. Keep up the great work!
Those who say "I can't do math" has never seen these alternate techniques. Not only are they efficient but a lot of fun to play around with. Wish schools taught this. Even if it's after learning the basic fundamentals first.
Those who say "I can't do math" have never seen these techniques because they don't enjoy doing maths. They also wouldn't think this is fun to play around with.
They do teach this people are just too dumb to apply it to real life this is (a+b)^2 it’s taught in 6th grade in most places
Thanks, man! You've made my math practice easier!😀
Great. Will keep practicing mental calculations. This greatly simplifies squares, yet still aiming at 1 min for 3-digit ones. Awesome practice. Thank you.
I love your videos, now I see why I had a rough time with math all these years. Even though I scored A's in Science, Health, History, English, Social Studies et. al.
I always enjoy sharing these with my class. Big thumbs up!
yea its fun when they look at u how fast u have done this but actually we r using these tricks to do faster .... :)
I like the way you work out these equations. I work the numbers on the side and add them. I have become hooked on working these math problems.
you are like my elementary school math teacher long long time ago...make the students enjoy math...thanks again 👏👌
Loved it. I really enjoyed the video. I hope you stay safe.
Thanks for the very clear instructions and showing how it’s done simply. I’ve now picked 50 random examples I intend to use these as a tool to learn better. I’m hoping this educates and helps me better my knowledge and grasp it. Thank you.
Thanks , it helped me a lot for finding the square of a number
I'm rubbish at maths but find this easy to follow, unlike when I was in school and regularly had the board duster thrown at me by the maths teacher for getting it wrong!! Thank you
3:38, analytical proof:
Let's "x" be the two digit num which is = (10a + b) where a and b are the corresponding digits of that number.
Thus, x = (10a + b)
Now let's square it,
=> x² = (10a + b)²
Therefore, x² = (100a² + b² + 20ab) ---(i)
Clearly, from (i) you can already see that, it is nothing but the sum of the squares of '10a', 'b' and, the twice the product of '10a' and 'b'
i.e. x² = (10a + b)² = [ *(10a)²* + *(b)²* + *2(10a)(b)* ]
Now you'll notice that you had to take 10 times of 'a', that's because a is in the Ten's place, for example 12 = 1×10 + 2, just like that.
so upon squaring you'll obviously get a 4 digit number, let's see how!
w.k.t, if x be a two digit number, then:
x² = *(100a² + b²) + 2(10a × b)*
a = Ten's digit, b = Unit's digit.
Let's take x = 69 for fun.
Now let's find out it's square.
69² = 100×36 + 81 + 2(10×6 × 9)
= 3600 + 81 + 2(10×6 × 9)
= *3681 + 2(6×9)×10*
= *3681 + 56×10*
Or,
*3 6 8 1*
+0 *5 6* 0
------------------
4 2 4 1 ← yes that's the answer! (10×[{(420)}] + 41 :P jk)
Now ↑ above you'll notice that 3681 is nothing but 36 or 6² and 81 or 9² !!!
And also, we get "0560" below 3681 because 560 is in hundred's place so it shits to the right side, but 560 also have a "0" in the last, so we see that the number "56" stays right below 68 in 3681 and that's what happens everytime with all two digit number squared!!!
And now you know exactly why it happens :)
Absolutely Incredible, thank you!
Great stuff! As a math guy, you're AWESOME 😎! I love your UA-cam channel. Keep up the GREAT WORK!
Very helpful mathematics teacher. Keep going up👍
My great grandson is going to love me sharing this with him. Thank you so much.
It's actually possible to extend this to numbers with 4 digits as well. If we take number like (512)² and write it like abc² your pyramid looks like a² b² c² 2ab 2bc 2ac like he showed us in the video. But if you have a number like 1234² you can do this as well. Your pyramid should then look something like this: a² b² c² d² 2ab 2bc 2cd 2ac 2bd 2ad. Really cool!
Can you explain the last part in pyramid form?
works with 5 digits too
This helps so much! I'm using this in my math test tomorrow. Thank You!
We need a techmath mental math app
Yes!
You sir are an excellent teacher. I dropped out of high school before finishing and later in my late 30's I was disabled and attended university on a rehab scholarship. Having not been exposed to anything beyond simple addition, subtraction, multiplication and division, I struggled with algebra, trig, and had to start out with remedial or high school math. If I had had a teacher as yourself I would have finished with a perfect 4.0 GPA as math is the only subject I didn't get straight A's in. Because of my lack of math background I had to settle for a 3.85 GPA.
Thanks for the mini-biography
Sir I really can't express in words how helpful your videos are . Respect
This was awesome!!! Will be teaching my kids your techniques
This channel makes me happy because now, if I learn these methods, I can be successful at everyday maths, instead of being anxious and very slow. Thank you!
this is literally (a+b)^2 haha
Literally. Good observation
he told that already like twice
@@tecmath To justify no idea because I have not learned algebra yet
Go to 4D space time by AK science
Yes it’s (a+b)^2
That’s Cool. I had no idea that they’re different ways to do this fast. Thank You!
very cool method. thank you. love your way of teaching. I could listen to your lessons all day :-)
(a + b) ^2 == a^2 + 2ab + b^2 (with 2 figures). (a + b + c)^2 = a^2 + 2ab +2bc + 2ac + b^2 + c^2 (with 3 figures). Although I knew these formulas, I had not figured out how to do this calculation in practice: thank you! I used to have another method that you can use for numbers as long as you know some of the lower squares by heart. If x^2 is the square you need, you use (x - a)(x + a) + a^2. I call it the harmonica because it works like a harmonica. It works like this. You have f.e. 17 = 20 x 14 + 3^2 = 289. Btw, this trick I got from my granddad (an illiterate fisherman, but he knew squares). I will admit, not as easy to use as your trick for larger number, because you end up with a smaller square. So doing 407 would be a little harder: 407^2 = 400 x 414 + 7^2 = 4 x 41400 + 49 = 165600 + 49 = 165649. Not as easy, but still, I used it for a long time. thanks for the tips and the video!
That’s nice. Been using it for a long time myself. You can do larger numbers if you adapt it slightly - see my videos on my channel if you would like!
Nice method
doing that since elementary school for all multiplication, squares included, pretty damn nice
always great to learn as many tricks to help out.
Just started watching these vids. Great help, ty
this guy taught me more mental math in 15 minutes of his content than my school did in 13 years of maths class
I tried it on numbers with 4 or more digits and this technic works there as well. As explained in another comment, this is just another way to visualize (a+b)^2.
ex: 4567^2
16253649 : a^2, b^2, c^2, d^2
406084 : 2ab, 2bc, 2cd
4870 : 2ac, 2bd
56 : 2ad
= 20,857,489
what about a bigger number like 989…?
G'day Josh, love your vids. short and sweet, no bs. cheers
Really wish I had a math teacher like you in highschool. Definitely made this easier.
Love the ones with the "0" in the middle.
Had to make sure this wasn’t an April’s fools video lol thank you so much!
Lol
Sorry to reply lateeeeee
I actually do feel smarter. I really love your channel and thank you so very much !❤
This was so helpful! This makes it soo easy!
If you keep showing these tricks, I'll never be able to leave the computer--I'll starve to death!
Is there a special trick for no.s like 888 or 99, or 666,. Or 77 etc?
@@stevenbrock528 for numbers all 9s you can do 99^2= 10000-199
999^2=1,000,000-1999
9999^2=100,000,000-19999
I arrived at this trick but you picturised it first ,BRAVO CONGRATULATIONS
Just started my pre electrical apprenticeship and your videos are very helpful!
What if the number is for example 998,in second step 81× 2 gives 162 ,and also 72×2 gives 144, how do you do these numbers?
Had to look at this and figure it out...it gets sloppy. You put the two numbers together but add the one's digit from 162 to the hundred's digit of 144 together getting 16344 and like standard math this goes below the first number shifting one to the left (leaving a space under the 1's digit) the other 144 in the third row is once again shifted another row leaving an empty space under the 10's digit. It might be easier to figure out than the standard squaring method, but I don't think I could do this in 5 seconds in my head.
Can you please explain this on paper 📜
You use (1000-2)² instead of the (a+b)²
This is essentially how you multiply numbers on paper normally, with a couple shortcuts to make it easier. Nice job i like this :)
Wow, this is actually amazing, thank you!
Absolutely love your voice explaining it to us.
Helpful 👍
This guy earned my sub, his videos are goddamn worth watching
Honestly helping me so much as I am practicing for my ASVAB for the marines
Very much thanks, you're the best math teacher!
Genius 👏🏼
This is Vedic maths
This is simple algebra
Watching these videos is far more convenient than reading books about Vedic arithmetic. Cheers!
Thanks you so much. This will save my time
Me who use a calculator to calculate 1+1 : interesting
😅Bruh same
That. Is. Great.
I haven't enjoyed math since the 60's! If I'd had that, I might have made it to algebra...
thanks, really helped me in my 2 digit squares and the technique was unknown to me previously
Thanks, that was very informative and fun. I'm feeling really smart right now.
omg I was practicing squaring 3 digit numbers and as soon as I wrote down 632 i heard him say 362, it was so close!
My call was 367
632²=360000+900+4+36000+2400+120=399424 there ya go. It's an old mathematical trick. Not hard at all. It's so old that I bet all of you actually knew it before the video, without realizing it. (a+b) × (a+b) = a²+2ab+b² It holds true no matter which base you use. And let's show an example of 23² = 20² + 2×20×3 + 3² or 400+120+9 aka 529.
It's how everyone turns big multiplications into smaller ones.
322*345 is difficult but 300*345 + 20*345 + 2*345 looks a lot easier and 300*300 + 300*40 + 300*5 + 20*300 + 20*40 + 20*5 + 2*300 + 2*40 + 2*5 looks even simpler to do.
And for the sake of answering that it's 90000+12000+1500+6000+800+100+600+80+10 or 111090. It's exactly the same principle.
I was stunned I got 362 as my guess!!!! xxxx
@@livedandletdie Feeling a dimmy wit at the 2ab stage as to me that is doubling and not squaring. Maths always was my weakest subject and still is along with needlework!!! xxxx
@@janemccourt5022 My needlework needs improvement, thankfully my maths is very good.
Looking at it as an algebraic equation just makes it easier. e.g.
Like someone mentioned (a+b)^2 or ².
Yeah exactly! (a+b)² = a² + 2ab + b².
I'd rather do it like this though
512² -> (500+12)²
= (500)² + 2(500)(12) + (12)²
= 250,000 + 12,000 + 144
= 262,144
It's kinda easier to digest. But either way works.
I agree!
Such a great methode. Thanks for that. Its nice to learn such stuff
Mesmerizing tricks. This will definitely help me in my GRE quant
He seems to be laughing always while talking or more likely is gonna burst into laughter but somehow getting everything together
Whee! That was fun. I hadn't played like this since 7the grade, and that was decades ago.
Hehe 54
47 years ago for me my how the time has flown, just amazed at how old I have gotten, it was just yesterday I was learning this in math class LOL
You're a fantastic teacher!
Loved that technique.
And you make math fun too!! ✌️
(a+b)^2=a^2+b^2+2ab. SIMILARILY,
67^2 can be written as (60+7)^2= 60*60+7*7+2*60*7= 4489
The order of the calculations is important as it relates to the tens column that the answer should be in. For example 60*60=3600 2*(60*7)=840 7*7=49.
However by using commas to denote the separation between the powers of 10 (lets call them open numbers) it enables one to handle the multiplication of any number of digits provided the correct sequence of numbers that are multiplied together are added together. In this case it would be 6*6=36, 2*(6*7)=84, 7*7=49 giving the open number result 36,84,49. From this it can be seen that the compressed number answer in Hindu-Arabic notation is 4489.
The problem comes from teaching long multiplication in columnar form and only allowing each column to contain one digit. This requires one to handle the carry (or compression of the open number result) in the middle of all the multiplication operations. If one turns the multiplication sum on its side and uses open numbers the process suddenly becomes a lot easier and quicker to perform as one can extend the power of 10 number calculations to handle results with more than one digit. This has the benefit of leaving the compression of the final open number result to the end of the process. Thus the order of operations can be done either right to left (traditional) or left to right (for mental speed maths) provided one is clear about which digit multiplications for each power of ten computation should be added together. For example
Units: 7x7 = 49
Tens: 6x7+7x6 = 84
100's: 6x6 = 36
result: [36,84,49] = 4489
@@sharonjuniorchess Thankyou for this effort !
Appreciated!
This is amazing and even more fun! ty!
thanks, this really helped me a lot!
Hi Josh, thanks for an easy explanation on squaring numbers up to 1000. I don't recall this type of explanation in any of my early schooling or tuition, which I shall now say it was knowledge denied. For this expanation, you deserve an A+🌟🌟🌟🌟🌟👏👍🥇.
Thank you for your like 👍. Pleasing comments and questions always appreciated.
Thanks mate
@@tecmath 👍📐Cheers.
Good trick, but you don't have to stop at 1000. To square a four-digit number:
The first row has the squares of each of the four digits, as with the three-digit numbers.
For the second row, multiply the adjacent digits and double the result, again as with the three-digit numbers. For example, with 2357, the second row becomes 061535. The only minor complication comes when any result is more than 100, in which case remember to carry the 1.
For the third row, multiply the first and third digits and double the result, then multiply the second and fourth digits and double the result. Again, remember to carry the 1 whenever a result exceeds 100.
For the (new) fourth row, multiply the first and last digits and double the result.
This technique can generalized for squaring any number with n digits. In the spirit of all math textbooks, this is left as an exercise for the student. 😀
carry the 1 where though? To the next row?
@@arpanmascarenhas1048 Just remember that each new number goes into the next two positions. With a three-digit number, think of the third digit as overflow. For example, to square 6789:
The first row is 36496481, the square of each digit.
For the second row, start with 6×7×2=84. Add to that 7×8×2=112, when, with two spaces reserved for this new number, you now have 8512 in this row. Then add 8×9×2=144 the same way, making this row 851344. I'll add a zero to the end to make the numbers align more clearly, making the second row 8513440.
The third row starts with 6×8×2=96. Then add 7×9×2=126, giving 9726. Add two zeroes for alignment, making this row 972600.
For the fourth row, you have 6×9×2=108 plus three zeroes for alignment, giving 108000.
Adding them up, you get 36496481 + 8513440 + 972600 + 108000 = 46090521, and you're done.
@@zanti4132 Wow ok this was very helpful.. Thank you! Can I reach out to you on instagram?
I dobt get it please help! With graphic
hey i did try the way you mentioned but i am unable to get the right answer if you are available to reply back. please do
Love coming back here
I caught on to this pretty fast. Thanks for the fun🤗💚
Me before I watched this: how does he explain a 5-second method in ten minutes -_-
Why not, we all love it
I'm 73 and left school in year 9. I failed math in the three years of high school that I did. I wish I'd known all these ways of doing math easily way back then, I think I would have blitzed it. Thanks for making it so much fun. LOL now I can't get enough of them. 😁
this helped me so much! thank you
I enjoyed doing it. Thank you
I have a question how about d square of 696 where do u write d product if 6 and 9 doubled that will be a 3 digit number
same with 999 squared
@@urvi7384 It actually does work for 999, you just have to contract the number. If you did this correctly, you get 162162 in the middle. What you have to do is add the two numbers in the middle to get 16362. The catch is that you have to line it up with the 818181. At the end you get 818181+163620+162 = 998001 which is 999^2. The same applies to 696.
@@urvi7384 there's an easier method there.
The concept being used in the video is to expand it as a binomial or a trinomial and just using the appropriate number of zeros. There's another trick: use a-b for numbers close but lesser than multiple of 10, 100.
Like 696^2 = (700 - 4)^2... So 490000 + 16 - 5600 = 484416
999^2 = (1000 - 1)^2... This becomes 1000000 + 1 - 2000 = 998001
The last digit of the 3 digit number would go in the same position as the last digit when it is 2 digits. So the first 108 would go directly under 368 and the second 108 would go below the 813. That way the last digits are still under the 8 and the 3.
@@shravyaboggarapu5877 And I'm like close encounters of the third kind.
I homeschool my son and this guy has made it so much easier teaching him. Thanks
yet another squaring method from you that caught my attention, thank you!
I have no words to thank you for teaching this superb method