how this works? solution: x^2 - y^2 + y^2 = x^2 (x+y)(x-y) + y^2 = x^2 we take y such that x+y or x-y ends in 0 for simplifying the arithmetic wow!! such a simple thing works so efficiently really it has reduced the mental efforts so much that I feel it should be called a trick.
For 48 square, just simple steps, 48 is 50 - 2. So subtract 2 from 25, we get 23 and now write the square of the number 2 at the end, that is 04 and hence getting the answer as 2304. Similar shortcuts are awesome and can be extended to square of any number till 125.
You could also do a similar thing for numbers near 500. Get the first three digits by subtracting 250 and the last three by squaring the difference from 500. E.g 492 squared = 242064 If the second part is more than three digits you would carry.
I hope to god you're not a teacher because you didn't explain that well at all. 48 is 50 - 2, so you take HALF of 50? (Edit; someone explained it better below)
@@tonybarfridge4369 25 is the square of 5 Since here any no. between 41 and 49 will be less than 2500 after squared .. After that apply the method shown and you will get the answer easily
I made a video of this but yours was clear when it comes to the explanation. I will choose right words when making another video. Thanks for the video i love it.
Why this method worked on two digits number can be explained with below quadratic equation ! 23^2 = (20 + 3) ^ 2 ==> expand above using (a+b)^2 = a^2 + 2*a*b + b^2 => 20^2 + 2 * 20 * 3 + 3^2 ==> take out 20 as common factor from first two terms ==> 20 (20 + 6 ) + 3^2 ==> 20 * 26 + 3 ^ 2 ==> Thus the above trick is another way of expressing quadratic equation!
I'm 21 years old currently re sitting my lvl 2 maths for my apprenticeship and I got to say I learned more from your videos then I ever did from school also you explain things or at least try the simple way and your voice just so calm it's amazing thank you 👍
I like the trick for squaring numbers close to 50. Get the difference between the number and 50, add that difference to 25, then square the difference and add it on (always 2 digits). e.g.: 56^2 : Difference is +6. 25+6 = 31. Append 6^2 = 36. Answer = 3136 48^2 : Difference is -2. 25-2 = 23. Append 2^2 = 04. Answer = 2304 This works nice and easily for numbers 41 to 59. It can be used for lower and higher numbers, but then you're into the realm of carrying.
This was wicked.. I love maths but how you simplify it to make it easier to work out is great.. the 27sq was the only one I got slightly confused by. But only because I came to 6849 but knew it wasn’t right because I knew the 65sq was correct and the 27sq couldn’t be higher than that Really like these
You're not wrong. He didn't explain that one at all. I think when you're squaring a number OVER 5 (27 is over 25), you have to carry. So 28^2 trick would be: 1. Difference from 20 is 8 2. 20 x 36 = 36 times two times ten = 720 3. 8^2 is 64. But you don't get 7264 lol, you do 720 + 64, which is 784. BOOM. (happy I got it)
For the second example I used 8 as the distance which gave me 40 x 56, 10 x 56 = 560, 4 x 500 = 2000, 4 x 60 = 240, 8² = 64, 2000 + 240 + 64 = 2304, how did I get do this correctly even though I diverted from what I was supposed to do?
This trick is not working for 72 square.. Acc to the method shown in video - Nearest tens number - 70 Difference - +2 Add the Difference to original number - 74 So 74*70=5180 But we have leave 2 spaces blank so 51__ Now append the square of the difference which is 2 so finally answer is 5104 But actually the square is 5184 Can anyone explain this to me ??
Other Way: Let Say the number is 82: 82^2 Now, 8*2*2*10 = 320 8^2 = 64 2^2 = 04 So we write this as 6404 Now 6404 + 320 =6724 Therefore: 82^2 = 6724 Easy?
If a 2 digit number is (10x + y) where x and y represent the digits, what we're actually doing is: 10x + y - y = 10x 10x + y + y = 10x + 2y 10x * (10x + 2y) = 100x^2 + 20xy Then y^2 + 100x^2 + 20xy Or: (10x+y)^2 = (10x+y)(10x+y) = 100x^2 + 10xy + 10xy + y^2 = 100x^2 + 20xy + y^2 Of course, you don't _have_ to do it to the nearest 10. It'd work the same way either way. For example, for 23^2: 23 + 7 = 30 23 - 7 = 16 30 x 16 = 480 7^2 = 49 480 + 49 = 529 Infact, it doesn't really matter what you do. You don't even have to do it to the nearest 10. As long as you take the original number, and multiply it by two numbers that are above or below the original number by the same amount, then add the square of the distance from the original number. In other words: 23 + y = 23+y 23 - y = 23-y (23+y)(23-y) = 529 - y^2 Then obviously when you add the y^2, it just becomes 529. Is there a similar (but more compilcated) method for 3 digit numbers though? Generally, we're working out (100x+10y+z)^2 which, after expanding the brackets, is 10000x^2 + 2000xy + 200xz + 100y^2 + 20yz + z^2 First, we square the 100x part to get 10000x^2 Then we square the whole of 10y+z to get 100y^2 + 20yz + z^2 Then we multiply the x by 10y+z to get 10xy + xz, and then double that, to get 20xy + 2xz If we add all this, so far, we get: 10000x^2 + 20xy + 2xz + 100y^2 + 20yz + z^2 (let's make this entire expression equal to a single variable of w) This obviously isn't the answer yet: If we subtract the full expanded answer of (100x+10y+z)^2 from the above, we get: (10000x^2 + 2000xy + 200xz + 100y^2 + 20yz + z^2) - (10000x^2 + 20xy + 2xz + 100y^2 + 20yz + z^2) = 1980xy + 198xz Or, keeping all coefficients as powers of 10: 1000xy + 1000xy - 10xy - 10xy + 100xz + 100xz - xz - xz, or, more simplified: 2(1000xy - 10xy) + 2(100xz - xz), or in more English form: Take the first 2 digits and multiply them. Then double the result, and subtract 10 times that number from 1000 times that number. Then, take the first and last digit and multiply them. Then double the result, and subtract that number from 100 times that number Then add those results together. Then add all of that to whatever you got from w earlier. Of course, the above algebraic generalisation is _much_ more complicated-sounding than an actual numerical example, so: Let's say 345^2. Take the 300 and square it to get 90000. Take the 45, and square it (using the method in this video, or any other method of squaring 2 digit numbers) to get 2025. Multiply the 3 by 45 to get 135. Now double this to get 270. Add all this to get 90000 + 2025 + 270 = 92295 Then, multiply the 3 and 4 to get 12. Double this to get 24. Take 240 (10x24) from 24000 (1000x24) to get 23760 Multiply the 3 and the 5 to get 15 Double this to get 30 Take 30 from 3000 (100x30) to get 2970 Add 92295 + 23760 + 2970 to get 119025 Which is equal to 345^2
I'm sure your videos are great for many purposes, and I can see you're having an impact on many people. But this title is absolute bull-manure. What a waste of 12 minutes. Hope you don't encounter ANY misfortune. (Not serious about the implied bad wishes, just making a point through word play.)
This is an old vedic math trick, based on the idea of the perfect square formula...so I'm sure to accept your apology in advance. BTW the funniest thing of all is you think Arthur Benjiman invented this idea...but here goes then... "I apologise for making a video on a concept that was invented hundreds of years ago and making a video about"
For the fourth trick a fun fact is that 111 million 111 thousand 111 squared is 12345678987654321 which is a palindrome like every other 111… squared number just that it goes up to 9 although idk what the next one would be 1….909….1? Or could be 1….919….1 lol if someone knows pls tell me cuz it ain’t like I can do that in a calculator haha
how this works?
solution:
x^2 - y^2 + y^2 = x^2
(x+y)(x-y) + y^2 = x^2
we take y such that x+y or x-y ends in 0 for simplifying the arithmetic
wow!! such a simple thing works so efficiently
really it has reduced the mental efforts so much that I feel it should be called a trick.
For 48 square, just simple steps, 48 is 50 - 2. So subtract 2 from 25, we get 23 and now write the square of the number 2 at the end, that is 04 and hence getting the answer as 2304. Similar shortcuts are awesome and can be extended to square of any number till 125.
You could also do a similar thing for numbers near 500. Get the first three digits by subtracting 250 and the last three by squaring the difference from 500. E.g 492 squared = 242064
If the second part is more than three digits you would carry.
This is far from clear.
I hope to god you're not a teacher because you didn't explain that well at all. 48 is 50 - 2, so you take HALF of 50? (Edit; someone explained it better below)
@@tonybarfridge4369
25 is the square of 5
Since here any no. between 41 and 49 will be less than 2500 after squared ..
After that apply the method shown and you will get the answer easily
What about 98
I made a video of this but yours was clear when it comes to the explanation. I will choose right words when making another video. Thanks for the video i love it.
You won't realise it but you surely helped competitive exam aspirants big time dude...
Why this method worked on two digits number can be explained with below quadratic equation !
23^2 = (20 + 3) ^ 2
==> expand above using (a+b)^2 = a^2 + 2*a*b + b^2
=> 20^2 + 2 * 20 * 3 + 3^2
==> take out 20 as common factor from first two terms
==> 20 (20 + 6 ) + 3^2
==> 20 * 26 + 3 ^ 2
==> Thus the above trick is another way of expressing quadratic equation!
On the example with 27²
It is easier to use 3 and make 30*24=720 plus 3²=9 gives 729
Its also so beautiful that both ways give the same result
yeah and since it was a little hard for me to do 30*24 I just did 60*12
I'm 21 years old currently re sitting my lvl 2 maths for my apprenticeship and I got to say I learned more from your videos then I ever did from school also you explain things or at least try the simple way and your voice just so calm it's amazing thank you 👍
Thank you so much! Your videos really help me, and the tricks are so useful.
I like the trick for squaring numbers close to 50.
Get the difference between the number and 50, add that difference to 25, then square the difference and add it on (always 2 digits).
e.g.:
56^2 : Difference is +6. 25+6 = 31. Append 6^2 = 36. Answer = 3136
48^2 : Difference is -2. 25-2 = 23. Append 2^2 = 04. Answer = 2304
This works nice and easily for numbers 41 to 59. It can be used for lower and higher numbers, but then you're into the realm of carrying.
it helps to explain why 25 is used, as it's taken from 50^2, but also because 50 is half of 100 as 25 is half of 50
Thank you for the video.
Now I can do the squaring in my head for fun !
This is great. I can finally learn how to do squares in my head
Wow! *441* views, *64* likes, and *1* dislike
All square numbers
You are the best commenter ever!
Currently 576 views, 81 likes and 1 dislike 0w0
This is no coincidence
currently 20773 views which is almost 144 which is 12 squared
This was wicked.. I love maths but how you simplify it to make it easier to work out is great.. the 27sq was the only one I got slightly confused by. But only because I came to 6849 but knew it wasn’t right because I knew the 65sq was correct and the 27sq couldn’t be higher than that
Really like these
You're not wrong. He didn't explain that one at all. I think when you're squaring a number OVER 5 (27 is over 25), you have to carry. So 28^2 trick would be:
1. Difference from 20 is 8
2. 20 x 36 = 36 times two times ten = 720
3. 8^2 is 64. But you don't get 7264 lol, you do 720 + 64, which is 784. BOOM. (happy I got it)
@@EmpyreanLightASMR 28^2= 14^2x2x2 😀
The second trick is the best. Thanks.
Bro thanks man my maths is really weak a nd my mental maths is far worse so you just saved my life when my exams are just around the corner
YOU HELPED SO MUCH might actually get a 90 this term
Hi sir you are doing a great job...keep it up!
Best stuff to learn from home during the pandemic
All is vedik maths bro
Hi thanks so much for this video. but in future videos could you do more tests like quizes to see what we've learnt.
These tricks are so useful to us
Thank you sir !!
Please upload a video on multiplying 3 digit number with 2 digit number
Please 😫🙏🙏💓
Thank you so much your video really helped me ,🥰🥰🥰🥰🥰
Youre so underrated tbh.
Thanks mate.
Love it!!! Brilliant!! Who in bloody hell left a dislike?? Bollocks!!
You have changed my life! I'm not joking either!
That 1111 square is very helpful. Thank you
All vedik maths
For the second example I used 8 as the distance which gave me 40 x 56, 10 x 56 = 560, 4 x 500 = 2000, 4 x 60 = 240, 8² = 64, 2000 + 240 + 64 = 2304, how did I get do this correctly even though I diverted from what I was supposed to do?
please could you do a video for doing square routes?
Math is Fasinating!!!
27^2 is actually easier if you compare to 30. 30 × 24 is 720 + 3^2, or 9, thus 729.
I love your videos
This video was great
Very good
Tecmath, we can also use (A+B)^2. Like 23^2 = (20 + 3)^2 and everybody know the formula
Best video of yourbchanel
Nice
11:15 my answer for 27 squared is different.
24*30=720
7*7=49
720+49=769
Can someone explain why my answer is different have I done something wrong?
@Corey McDonald ok. I thought we have to square the last number. Thx for the explanation.
you give two method(video) on squaring a number but the other one doesn t fit in the example you give here
Im so confusedddd
same here, i keep trying but getting different numbers for both methods
What is a squared number? Is it a shortcut?
try 192 squre in any trick.
This trick is not working for 72 square..
Acc to the method shown in video -
Nearest tens number - 70
Difference - +2
Add the Difference to original number - 74
So 74*70=5180
But we have leave 2 spaces blank so 51__
Now append the square of the difference which is 2
so finally answer is 5104
But actually the square is 5184
Can anyone explain this to me ??
Other Way:
Let Say the number is 82:
82^2
Now,
8*2*2*10 = 320
8^2 = 64
2^2 = 04
So we write this as 6404
Now
6404
+ 320
=6724
Therefore:
82^2 = 6724
Easy?
59²
So 5*9*2*10=900
5²=25
9²=81
2581+900=3481=59²
Wow thats cool, i wonder why this works.
@@cerwe8861 (a+b)² = a²+2ab+b²
Now, 59² = (50+9)² = 50² + 2*50*9 + 9²
If a 2 digit number is (10x + y) where x and y represent the digits, what we're actually doing is:
10x + y - y = 10x
10x + y + y = 10x + 2y
10x * (10x + 2y) = 100x^2 + 20xy
Then y^2 + 100x^2 + 20xy
Or: (10x+y)^2 = (10x+y)(10x+y) = 100x^2 + 10xy + 10xy + y^2 = 100x^2 + 20xy + y^2
Of course, you don't _have_ to do it to the nearest 10.
It'd work the same way either way. For example, for 23^2:
23 + 7 = 30
23 - 7 = 16
30 x 16 = 480
7^2 = 49
480 + 49 = 529
Infact, it doesn't really matter what you do. You don't even have to do it to the nearest 10.
As long as you take the original number, and multiply it by two numbers that are above or below the original number by the same amount, then add the square of the distance from the original number.
In other words:
23 + y = 23+y
23 - y = 23-y
(23+y)(23-y) = 529 - y^2
Then obviously when you add the y^2, it just becomes 529.
Is there a similar (but more compilcated) method for 3 digit numbers though?
Generally, we're working out (100x+10y+z)^2 which, after expanding the brackets, is 10000x^2 + 2000xy + 200xz + 100y^2 + 20yz + z^2
First, we square the 100x part to get 10000x^2
Then we square the whole of 10y+z to get 100y^2 + 20yz + z^2
Then we multiply the x by 10y+z to get 10xy + xz, and then double that, to get 20xy + 2xz
If we add all this, so far, we get: 10000x^2 + 20xy + 2xz + 100y^2 + 20yz + z^2 (let's make this entire expression equal to a single variable of w)
This obviously isn't the answer yet:
If we subtract the full expanded answer of (100x+10y+z)^2 from the above, we get:
(10000x^2 + 2000xy + 200xz + 100y^2 + 20yz + z^2) - (10000x^2 + 20xy + 2xz + 100y^2 + 20yz + z^2) = 1980xy + 198xz
Or, keeping all coefficients as powers of 10: 1000xy + 1000xy - 10xy - 10xy + 100xz + 100xz - xz - xz, or, more simplified:
2(1000xy - 10xy) + 2(100xz - xz), or in more English form:
Take the first 2 digits and multiply them. Then double the result, and subtract 10 times that number from 1000 times that number.
Then, take the first and last digit and multiply them. Then double the result, and subtract that number from 100 times that number
Then add those results together.
Then add all of that to whatever you got from w earlier.
Of course, the above algebraic generalisation is _much_ more complicated-sounding than an actual numerical example, so:
Let's say 345^2.
Take the 300 and square it to get 90000.
Take the 45, and square it (using the method in this video, or any other method of squaring 2 digit numbers) to get 2025.
Multiply the 3 by 45 to get 135.
Now double this to get 270.
Add all this to get 90000 + 2025 + 270 = 92295
Then, multiply the 3 and 4 to get 12.
Double this to get 24.
Take 240 (10x24) from 24000 (1000x24) to get 23760
Multiply the 3 and the 5 to get 15
Double this to get 30
Take 30 from 3000 (100x30) to get 2970
Add 92295 + 23760 + 2970 to get 119025
Which is equal to 345^2
Hi. I like your trick but second trick of squaring doesn't work on below 30. That is so sad
❌This is wrong! I betcha!!
There is a number that can't be squared by this way.
It's numbers ending with '6'.
Try it
16²
36²
23^2
_ _3^2=_ _ 9
(23+3) ×2=52_
23^2=529
Well, I'll be buggered.
First comment...😊
@Gavin Singh hello
but what if the number was 74? the method does not work
someone help
Why this video has very low views!!!
this is crazy
Yay
you are BADD!
🙃
I'm sure your videos are great for many purposes, and I can see you're having an impact on many people. But this title is absolute bull-manure. What a waste of 12 minutes. Hope you don't encounter ANY misfortune.
(Not serious about the implied bad wishes, just making a point through word play.)
Hahaha at least give credit to Arthur T. Benjamin... Or to whoever you "stole" that trick from.
This is an old vedic math trick, based on the idea of the perfect square formula...so I'm sure to accept your apology in advance.
BTW the funniest thing of all is you think Arthur Benjiman invented this idea...but here goes then... "I apologise for making a video on a concept that was invented hundreds of years ago and making a video about"
Yeah he didnt steal it, the indian vedic mathematicians invented this stuff. It's cool math wish they taught us this in school.
@@NaterNorris They don't even teach it here in India : |
For the fourth trick a fun fact is that 111 million 111 thousand 111 squared is 12345678987654321 which is a palindrome like every other 111… squared number just that it goes up to 9 although idk what the next one would be 1….909….1? Or could be 1….919….1 lol if someone knows pls tell me cuz it ain’t like I can do that in a calculator haha
Yay