Dear Dico for mentally doing 23^2 use the Base20. See the 3rd vid on Glad2teach website (link given below the vid above) 23 is at the distance of 3 from Base20 ( pls note that this distance 3 would be added initially and later its square would get added) Here I go step by step Step1: Add that 3 to 23. You get 26 (or 260) 0 indicates that one more place to go. Step2: Now double up 260 and add to it square of that distance 3 (that is 9) 520 + 9 = 529 (ANSWER) Shahryar (Glad2teach)
Dear Chamillionaire993, I use just 2 EasyCal techniques to perform all my multiplication mentally. 1) Base Multiplication 2) Rainbow Multiplication If the given number is far from any Base then of course you need to use Rainbow Multiplication. See the Video Response I have attached below. Incidently I was given the number 67 to multiply mentally in a Live Seminar ( see the video below ) Shahryar (Glad2teach)
@DanandDonna1 , thanks for pouring your heart out while writing your comment. Math if learnt the right way fills you with pure excitement and tranquility at the very same time. I wish to take you and other people who are struggling with Mathematics into the magical world of numbers. A guided tour till Infinity and back. Once the human mind gets the real taste of Mathematics then it keeps craving for more. Math is the workout for your brain ... it is addictive .
Drew2pac, thanks for adding your valuable comment !! Once again let me emphasise that knowledge is a Collective Heritage of our entire "Human" Race. As an Indian I am proud of what my Indian Ancestors have achieved but not in an arrogant manner. I am trying to make my own humble contribution to this ocean of knowledge on Mathematics. Rgds Shahryar (Glad2teach )
Dear math teacher, I love your youtube videos. I'm really grateful someone like you exists out there and is willing to share his knowledge with others. Thank you !
Stefan, 116 square can easily be calculated with Base Method I have shown above. 116 is at the distance of 16 from our base100. So 116 + 16 = 132 _ _ ( two more places to go) or 13200 Now we just need to put the square of 16 in those empty places ( in case you do not know then you can use base10 to calculate it to be 256 ) So 13200 + 256 = 13456 ( Final Answer) Watch 3rd EasyCal video on Glad2teach site to learn this Base Method (link given below the video above) Shahryar (G2t)
Dear hammas74, to see how to square the numbers near Base 50, see the 2nd video on Glad2teach website ( link below the video above ). 45^2 45 is at a distance of (minus) 5 from Base 50. So subtract that from 25, you get 20 _ _ ( you get first two Answer digits ) Now for the last 2 Answer digits, simple write the square of that distance (minus) 5 That is 25 So the final Answer of 45^2 = 2025 ( Ins't that easy !! ) Shahryar ( Glad2teach )
Glad that you liked this Easycal techniques ( from ancient Vedic Math of India ). This technique is called Base Multiplication. "Base" is a friendly number whose reference we take to multiply the unfriendly numbers close to it. Usually the powers of 10 make a good base ( like 10, 100, 1000, 10000 .... ) and so do some multiples of 10. To learn how to use easily other bases watch the 3rd EasyCal video on Glad2teach website ( link given below the video above ) Shahryar (Glad2teach)
i love your enthusiasm for math. This subject I can never understand and never will. Parents didn't care much to help and when one of my parents tried to help, she ended up screaming her head off, day after day because I don't GET it. Asked teachers and was lucky to get a minute with them. The school system failed me back then, 40yrs. ago, and doing worse now. That's where it lies.
This is an application of the formula (a+b)^2 = a^2 + 2ab + b^2. We just do 104^2 = (100 + 4)^2 = 10000 + 2*400 + 16. A similar example is 49^2 = (50 - 1)^2 = 2500 - 100 + 1 = 2401. Numbers closer to 100 work well because how well they fall into place.
CharlesIddesleigh, thanks for expressing your kind gratitude. 'Thank You' goes a long way. You should watch all the EasyCal videos on this CZcams channel and also there are 3 more free vids on glad2teach website (link given below the video above). You can build a strong foundation in fast Math. There is a paid tutorial as well ( full EasyCal Series on faster Arithmetic & Algebra) if you later become keen to take your skills to the next level. Best Wishes Shahryar Badar Khan (Glad2teach)
This is somewhat useful, but it becomes utterly pointless when your numbers go beyong the twenties below or above the 100 mark, as it requires increasingly difficult head multiplication. Not to mention it doesn't work for numbers below the 50 mark.
You should use Base50 to square or multiply any number near 50. See the 2nd EasyCal video on Glad2teach website (direct link given below the video above). Shahryar Badar Khan(Glad2teach)
@glad2teach i second that .... math is addictive when you understand it and you want more out of it. Also, TEACHING math is another one of my addictions!! Thanks so much for all the shortcuts!!! keep them coming :-P
I was looking for few videos for fast calculation. I am happy that Glad2teach is one among them. One thing I liked the most is the emphasis given on the word mentally.You guys meant it and stood by it. There are other crap videos who show complex methods and calculating in their method requires pen paper.I am interested for methods where I do everything mentally. Keep it up!!!
how u get 1016? when 100 x 100 is 10000. here is easy method 104 x104 4 x 4 = 16 100 x 4 = 400 x 2 = 800 (x2 because there are 2 100s and 2 4s) 100 x 100 = 10000 10000 + 800 + 16 = 10816 u can also do this way since 104 is close to 100 104 100 +4 100 +4 now if you add +4 to original number it will become 108 and 4 x 4 is 16 so answer is 10816
The title of the video says everything: it is about tricks, a kind of heuristics that you can use to solve real-world problems. Hence, they are quite useful - I can't think why someone would waste his/her time to attack a video like this! Our friend Shahryar is doing a good job by teaching these techniques for us!!
Dear eyeliner12sd, you have made a great start in Mathematics. Keep this momentum of learning going by regular practice. Soon you would become fluent with numbers. All the Best Shahryar ( Glad2teach )
Works as well in base 100, and in any base by the way. It's very simple to proove. We have "b" the base and "k" the difference between our actual number "x" and the base. We start with : x = b + k x^2 = (b+k)^2 = b^2+2bk+k^2 = b (b+2k) + k^2 = b ((b+k)+k) + k^2 = b(x+k)+k^2 So if we have 100 as our base : x^2=100*(x+k)+k^2 If we have 52, k = -48. 52^2 = 100*(52-48)+(-48)^2=400+2304=2704 We could do it with awkward bases like 42 to calculate the squared value of 324, although not useful.
Your harsh worded comment exudes your keenness to learn. To become a good student one has to become a good listener. Fast method I have shown is called Base Multiplication. If no. is close to a Base (friendly no.) we can square it easily. For 13 we would use Base10. For 987 it makes sense to use 1000 987 is 13 down from 1000. So subtract that 13 from 987 You get 974 _ _ _ . 3 more places to go ( as 1000 has 3 zeros). Simply put there square of 13 974 169 (Answer) Shahryar (Glad2teach)
Thanks for keeping the discussion erudite Ancient works of India I have referred to above were in Sanskrit (one of the oldest Languages). These books were translated in Arabic by great Arab Scholars like Khwārizmī (aka Algoritmi) & Al-Biruni which were then translated into Latin (English) These Arab Scholars gave credit where it belonged & called it Al-Arqam Al-Hind meaning Numerals of India. Great Fibonacci called it Modus-Indorum (Methods of India) in his famous book Liber Abaci Glad2teach
Knowledge is a collective heritage. 5000 years old Indus Valley Civilization (ancient India) has made remarkable contributions to this pool. 1) Hindu Numerals (our 10 digits from 0 to 9 ). No modern Math could be possible without them 2) Decimal Place Value System (Base 10). As you know Roman Counting was not Place Value thus highly difficult. 3) Pingala first used Binary System (Base 2). Without this there would have been no modern computing. No word limit left. Shahryar (Glad2teach)
@Chamillionaire993 I can see your point and I agree to some point, there will ALWAYS be certain numbers easier than others when it comes to head calculation, but 67 = (70 - 3) works just aswell, and it's not THAT much harder... For example: 70^2 - 2*3*70 + 3^2 = 4900 - 420 + 9 = 4489. The "hardest" part is remembering those 3 numbers before adding them together :)
Simple, sqaure will be of four digits _ _ _ _ Let your number is x Step 1: x-50 = a Step 2: 25+a = b Step 3: a^2 = c your square will be BC. e.g. your 56 is +6 of 50. So, 31(25+6)36(6^2) or 3136
I have always struggled with and been intimidate by math. This video has eased my anxiety and I am eager to learn and strengthen my math skills. Thank you so very much!
@GothicDarkhellrazor 7x7=49. 7, 14, 21, 28, 35, 42, 49. So for 107, you have 7 more than 100 so you add 7, giving you 114. Then put 7^2 (49) on the end giving you 11449.
I think the easiest way to do this kind of thing is to use distributive property. separate 100 into (100+4). then you know it's 100^2 + 2*100*4 + 4^2, all of which are pretty simple to figure out and add together, especially since 100^2 =10,000 isn't hard to keep in your memory at all.
There's another video posted for #'s 30-70. Same idea, but your base# is 50 instead of 100. Find the distance of the # from 50 ie: 40. 40 is 10 less than 50 so subtract 10 from 25 (1/2 of 50) and that is your first 2 digits (15) then find the root of that distance 10^2 =100 ....so 00 are the last 2 digits the 1 gets added to the 2nd digit 5 making the answer 1600!
@ahmadguitar87 The principle is "Squaring a binomial"... It implies that ANY 2-or-more-digit number can be written as a binomial and squared in a realy simple manner...
Essentially we can break the problem down into the following: 104*104 = (100 + 4)^2 the general form of (a+b)^2 = a^2 + 2ab + b^2 We can factor so that we get (a+2b)*a + b^2 Now, in the first example, a=100, so we can take (100+8) and add two zeroes, to get 10800, and add 4^2 to get 10816. Hope that this helped. I don't think that this method will work for >199, however maybe I missed something in the method used.
If it's an arithmetic sequence, then it can be expressed as a[n] = a[1] + (n-1)d, where a[1] is the initial term and d is the common difference. That said, we know that a[1]=16 and a[5]=17, so: 17 = 16 + 4d => d=1/4, and so we have the solution: a[n] = 16 + (n-1)/4.
@pinky93rocksm the reason you know that you have to add 2 additional digits, even if your starting under 100, is your equasion is being based off of the number 100. there are 2 additional digits after the primary, therefore you add 2 additional digits when you multiply. 2 x 2 = 4. just like if you went to use 1000 as a base instead, you would add an additional 3 digits. because 3 zeros. 3 x 3 = 6. hope this was helpful XD
In Germany, we call this Referenzmethode. It's especially easy with squares, but it works not only with squares, but also with numbers which are not too far away from each other like 98 x 97 and which are near to an easy-to-calculate-with reference number, like 100 or 1000.
It's because of the distributive law from elementary algebra. Do u remember high school, factoring quadratic equations? when you need to expand (4x - 5)^2 there was a shortcut instead of distributing, it's always (ax + k)^2 = a^2*x^2 + 2*k*a^2*x + k^2 I don't expect u to remember, but the same rule applies when ur squaring a number 112^2 = (100 + 12)^2 = (100^2 + 2*100*12 + 12^2)
Or you could 104 round to 100 104 - 100 = 3 104 + 4 = 108 100 x 108 + 4^2 =10816 This works with any number. Round to the nearest multiple of ten. Find difference. Subtract from original. Multiply two numbers. Add the difference squared.
@PlayerWaluigiii but you can only do the logarithm of a positive number so the answer -0.099=e^(x) can be eliminated. That leaves us with 10.099=e^(x) use logarithm to isolate x: x=[(log10.099)/(log(e^1))] x=2.31 I figured all of that out myself by the way. :)
@PlayerWaluigiii e^(2x)-10e^(x)-1=0 let e^(x) become "x" to simplify things for now. This gives us (x^2)-10x-1=0 use quadratic equation to find that 2 possible answers are 10.099 or -0.099 these answers are our "x", which is really e^(x). So, 10.099=e^(x) or -0.099=e^(x) then use logarithms to isolate the real x. See next reply.
@EvilBharathy yes it works, 115 + 15 = 130, 100--> 2 zeros, so 2 numbers to go after 130. 15*15=225. since this number has 3 digits the first one is added to the last digit of the first number (so 130 becomes 132) and the 25 becomes after that, so it becomes 13225. I hope I am explaining this the right way :)
I would suggest you watch the 3rd easycal video on glad2teach website (link given below the video above) for a more 'spirited' explanation of using the Base. All the Best Shahryar Badar Khan (Glad2teach)
you're right by making 104 into 100+4 then you square that so you have a polynomial (100+4)(100+4) then when you do polynomial multiplication you will end up adding 100000+400+400+16 which is the equivalence of adding 104+4 making it the first 3 digits and then adding 16 to the last 2 digits
this is nice sir but i have a question ! incase to solve (124) whole square according to u ,it will be 124 + 24 = 148 n then (24) square ...then how to solve (24) whole square as fast as u did
Start by writing down 25 (five squared), and then consider the first digit (left to right), which is five, and then multiply it by the next consecutive natural number, which is six, therefore, 5 x 6 = 30. Placing these answers together gives: 3025. Hope this helps.
or you could use FOIL for all numbers (first outside inside last) for example, 104^2 = (100+4)(100+4) = (100)(100) + (100)(4) + (4)(100) + (4)(4) = 10816
@PlayerWaluigiii Easy. Follow along. Each step is separated by a space. [e^(x)-e^(-x)]/2=5 e^(x)-e^(-x)=10 e^(x)-[1/(e^(x))]-10=0 common denominator [(e^(2x)/(e^(x))]-[1/(e^(x))]-[((10)e^(x))/(e^(x))]=0 now eliminate denominators by multiplying the denominator on both sides of the equation. See my next reply (not enough room in this one).
73-27 is 46. So then you square 27 which is 729 and add it to the 46 (which needs two extra digits). So, add 729 to 4600 which makes 5329. This method is only really useful if the number is closer to 100 as the video says otherwise you get bigger number to square like 27.
that is a nice idea, glad2teach! But for the particular case of 55*55, won't it be easier to use 25*11*11, since there is a very easy way to multiply by 11?... like 275*11=3025, even if you don't know the *11 trick, you can even do 2750+275, which is easy 3025!... Of course, there are many ways to solve for sort of any calculation and I am just suggesting flexibility and to be one with the spark and the solution, if you know what I mean!...
You could improve the video and add it some depth with the general formula (100+X)^2 = 10000 + 2*X*100 + X^2 As well as (100-X)^2 = 10000 - 2*X*100 + X^2 Digit separation works well when 0< X < 10 Btw, can you calculate 93*107 in five seconds? (100*100 - 7*7 = 9951) It is equally simple if not simpler : (100+X)*(100-X) = 100*100 - X*X
For 2-digit numbers, instead of using bases as a means of calculation what do you feel about the technique ab^2 = (a^2) (b^2) (not multiplication simply placing the 2 answers alongside) + the sum of (a+b)x2
You're videos are very helpful! Thank you for posting them! I wish I knew this stuff when I was in school so I would've had less homework and more play time! I am going to show your videos to my kids! Thanks again!
Thank you SO much for this. I'm in Algebra 2, and we're finishing chapter 6, which is polynomials. GOD, this is going to help me on the test- she's not letting us use calculators on the first part. YOU'RE MY HERO! (Btw I think your accent is kinda cool :). Just for all those jerks who're being mean about it)
you mean 3 digit numbesr? other 3 digit number are very easy too. If you mean 2 dgt no.s then, I can write it here: 34X34= 3x4x2(always two)so 3x4=12;x2=24, and add a zero (so 240) Second part: 3x3=9; 4x4=16; 9+16=916. Then add the first part to the second: 916+240=1156, 45x45: 4x5x20=400, 4x4+5x5=1625; 1625+400=2025, keep practicing :)
Sir, You are lecturing me on the history which no one denies. I respect that. I'm stating the facts in present time. Why would Indians, Chinese, etc. want to come to the US and study? because the standards are far higher - conceptual education. No one who has studied in Subcontinent denies that schools put emphasis on rote learning - unless they are being dishonest.
had to think about that the whole time! Then i tried different examples and found out the trick behind it... You always have to multiply with the first figure of the base and then add wahtever the square of your "distance from the base" is... Examples: 16^2 (base 10) --> 1*(16+6)=22_ ; 6^2=36 => answer: 256 24^2 (base 20) --> 2*(24+4)=56_ ; 4^2=16 => answer: 576 33^2 (base 30) --> 3*(33+3)=108_ ; 3^2=9 => answer: 1089 now you can go up to 99 and it will always work the same way!
Dear Dico for mentally doing 23^2 use the Base20.
See the 3rd vid on Glad2teach website (link given below the vid above)
23 is at the distance of 3 from Base20 ( pls note that this distance 3 would be added initially and later its square would get added)
Here I go step by step
Step1: Add that 3 to 23. You get 26 (or 260)
0 indicates that one more place to go.
Step2: Now double up 260 and add to it square of that distance 3 (that is 9)
520 + 9 = 529 (ANSWER)
Shahryar (Glad2teach)
Dear Chamillionaire993, I use just 2 EasyCal techniques to perform all my multiplication mentally.
1) Base Multiplication
2) Rainbow Multiplication
If the given number is far from any Base then of course you need to use Rainbow Multiplication.
See the Video Response I have attached below. Incidently I was given the number 67 to multiply mentally in a Live Seminar ( see the video below )
Shahryar (Glad2teach)
@DanandDonna1 , thanks for pouring your heart out while writing your comment. Math if learnt the right way fills you with pure excitement and tranquility at the very same time. I wish to take you and other people who are struggling with Mathematics into the magical world of numbers. A guided tour till Infinity and back. Once the human mind gets the real taste of Mathematics then it keeps craving for more. Math is the workout for your brain ... it is addictive .
Drew2pac, thanks for adding your valuable comment !!
Once again let me emphasise that knowledge is a Collective Heritage of our entire "Human" Race. As an Indian I am proud of what my Indian Ancestors have achieved but not in an arrogant manner. I am trying to make my own humble contribution to this ocean of knowledge on Mathematics.
Rgds
Shahryar (Glad2teach )
Dear math teacher, I love your youtube videos. I'm really grateful someone like you exists out there and is willing to share his knowledge with others.
Thank you !
and become a hero on class
I HAVE SEEN THIS TRICK 1ST TIME AND YOU ?
czcams.com/video/Xm9GUCT4vQE/video.html
Stefan, 116 square can easily be calculated with Base Method I have shown above.
116 is at the distance of 16 from our base100.
So 116 + 16 = 132 _ _ ( two more places to go) or 13200
Now we just need to put the square of 16 in those empty places ( in case you do not know then you can use base10 to calculate it to be 256 )
So 13200 + 256 = 13456 ( Final Answer)
Watch 3rd EasyCal video on Glad2teach site to learn this Base Method (link given below the video above)
Shahryar (G2t)
Dear hammas74, to see how to square the numbers near Base 50, see the 2nd video on Glad2teach website ( link below the video above ).
45^2
45 is at a distance of (minus) 5 from Base 50.
So subtract that from 25, you get 20 _ _ ( you get first two Answer digits )
Now for the last 2 Answer digits, simple write the square of that distance (minus) 5
That is 25
So the final Answer of 45^2 = 2025 ( Ins't that easy !! )
Shahryar ( Glad2teach )
You should have ended the video with: "Thank you, come again!"
This is AMAZING! Thank you , thank you, thank you!! This is going to help me out in my GCSE's and in general life so so much! :D
czcams.com/video/FrL8gqs2B8w/video.html
Glad that you liked this Easycal techniques ( from ancient Vedic Math of India ). This technique is called Base Multiplication.
"Base" is a friendly number whose reference we take to multiply the unfriendly numbers close to it. Usually the powers of 10 make a good base ( like 10, 100, 1000, 10000 .... ) and so do some multiples of 10.
To learn how to use easily other bases watch the 3rd EasyCal video on Glad2teach website ( link given below the video above )
Shahryar (Glad2teach)
i love your enthusiasm for math. This subject I can never understand and never will. Parents didn't care much to help and when one of my parents tried to help, she ended up screaming her head off, day after day because I don't GET it. Asked teachers and was lucky to get a minute with them. The school system failed me back then, 40yrs. ago, and doing worse now. That's where it lies.
or You can Do it with the binomic formal :
104^2
(100+4)^2
100^2+2*100*4+4^2
is that the shitty common core way? if so then im not using that
No both methods are wayyyyyy beyond core standards
Are you crazy it will take more than 5 sec bro!!
@@sciencehelp9693 not for me
omg thank you so much for this! amazing
@Stoners Club Records don't worry bro every youtuber has a secret power and mindsets
This is an application of the formula (a+b)^2 = a^2 + 2ab + b^2.
We just do 104^2 = (100 + 4)^2 = 10000 + 2*400 + 16.
A similar example is 49^2 = (50 - 1)^2 = 2500 - 100 + 1 = 2401.
Numbers closer to 100 work well because how well they fall into place.
CharlesIddesleigh, thanks for expressing your kind gratitude. 'Thank You' goes a long way. You should watch all the EasyCal videos on this CZcams channel and also there are 3 more free vids on glad2teach website (link given below the video above). You can build a strong foundation in fast Math.
There is a paid tutorial as well ( full EasyCal Series on faster Arithmetic & Algebra) if you later become keen to take your skills to the next level.
Best Wishes Shahryar Badar Khan (Glad2teach)
that was sick! now I will show my friends about it and they will be super amazed
lol
Don't show them. The less people who know, the better.
SHADOW X h
This is somewhat useful, but it becomes utterly pointless when your numbers go beyong the twenties below or above the 100 mark, as it requires increasingly difficult head multiplication. Not to mention it doesn't work for numbers below the 50 mark.
You should use Base50 to square or multiply any number near 50. See the 2nd EasyCal video on Glad2teach website (direct link given below the video above).
Shahryar Badar Khan(Glad2teach)
@glad2teach i second that .... math is addictive when you understand it and you want more out of it. Also, TEACHING math is another one of my addictions!! Thanks so much for all the shortcuts!!! keep them coming :-P
ur all the tricks are awesome and so easy but caN U ALSO GIVE ME A TRICK to remember all the trick for different sums
if da number, like previous comment, does range from 20-89, what do u do
Jelani Mays-Smith nowork
I was looking for few videos for fast calculation. I am happy that Glad2teach is one among them. One thing I liked the most is the emphasis given on the word mentally.You guys meant it and stood by it. There are other crap videos who show complex methods and calculating in their method requires pen paper.I am interested for methods where I do everything mentally. Keep it up!!!
It is been three years i have been as your fan..Satisfy and friendly Hats off you
genius!
I was like 1016 no wait 10016 FUUUUUUUUUUUUUUUUUUUUUUUU
how u get 1016? when 100 x 100 is 10000.
here is easy method
104
x104
4 x 4 = 16
100 x 4 = 400 x 2 = 800 (x2 because there are 2 100s and 2 4s)
100 x 100 = 10000
10000 + 800 + 16 = 10816
u can also do this way since 104 is close to 100
104
100 +4
100 +4
now if you add +4 to original number it will become 108 and 4 x 4 is 16
so answer is 10816
The title of the video says everything: it is about tricks, a kind of heuristics that you can use to solve real-world problems. Hence, they are quite useful - I can't think why someone would waste his/her time to attack a video like this!
Our friend Shahryar is doing a good job by teaching these techniques for us!!
It does work and it is very easy !! Use the right base (Base50). See the 2nd EasyCal video on glad2teach website ( link below the video above )
I did 103. So I did 103+3=106. So first 3 numbers is 106. Then 3^2 = 9 then I got 1069 as my answer, but it was actually 10609. Help please
103+3=106
3*3=9
always remember that 100 has two zero. 9 will become 09 then you will got the answer . 10609
OOPS, and thanks!
Dear eyeliner12sd, you have made a great start in Mathematics. Keep this momentum of learning going by regular practice. Soon you would become fluent with numbers.
All the Best
Shahryar ( Glad2teach )
Works as well in base 100, and in any base by the way. It's very simple to proove.
We have "b" the base and "k" the difference between our actual number "x" and the base.
We start with : x = b + k
x^2 = (b+k)^2 = b^2+2bk+k^2 = b (b+2k) + k^2 = b ((b+k)+k) + k^2 = b(x+k)+k^2
So if we have 100 as our base :
x^2=100*(x+k)+k^2
If we have 52, k = -48. 52^2 = 100*(52-48)+(-48)^2=400+2304=2704
We could do it with awkward bases like 42 to calculate the squared value of 324, although not useful.
Your harsh worded comment exudes your keenness to learn. To become a good student one has to become a good listener. Fast method I have shown is called Base Multiplication. If no. is close to a Base (friendly no.) we can square it easily.
For 13 we would use Base10. For 987 it makes sense to use 1000
987 is 13 down from 1000. So subtract that 13 from 987
You get 974 _ _ _ .
3 more places to go ( as 1000 has 3 zeros). Simply put there square of 13
974 169 (Answer)
Shahryar (Glad2teach)
Thanks for keeping the discussion erudite
Ancient works of India I have referred to above were in Sanskrit (one of the oldest Languages). These books were translated in Arabic by great Arab Scholars like Khwārizmī (aka Algoritmi) & Al-Biruni which were then translated into Latin (English)
These Arab Scholars gave credit where it belonged & called it Al-Arqam Al-Hind meaning Numerals of India. Great Fibonacci called it Modus-Indorum (Methods of India) in his famous book Liber Abaci
Glad2teach
Thanks !! If one is really keen to acquire knowledge then all the hurdles can be overcome.
All the Best - Shahryar ( Glad2teach )
Knowledge is a collective heritage. 5000 years old Indus Valley Civilization (ancient India) has made remarkable contributions to this pool.
1) Hindu Numerals (our 10 digits from 0 to 9 ). No modern Math could be possible without them
2) Decimal Place Value System (Base 10). As you know Roman Counting was not Place Value thus highly difficult.
3) Pingala first used Binary System (Base 2). Without this there would have been no modern computing.
No word limit left.
Shahryar (Glad2teach)
@Chamillionaire993 I can see your point and I agree to some point, there will ALWAYS be certain numbers easier than others when it comes to head calculation, but 67 = (70 - 3) works just aswell, and it's not THAT much harder... For example:
70^2 - 2*3*70 + 3^2 = 4900 - 420 + 9 = 4489.
The "hardest" part is remembering those 3 numbers before adding them together :)
for squaring, you can also do this: 3^2=9 sqr9 3 3+4(next number)=7 9+7=16 or 4^2. If you know the one prior, you can do this even faster.
Simple, sqaure will be of four digits _ _ _ _
Let your number is x
Step 1: x-50 = a
Step 2: 25+a = b
Step 3: a^2 = c
your square will be BC.
e.g. your 56 is +6 of 50. So, 31(25+6)36(6^2) or 3136
I have always struggled with and been intimidate by math. This video has eased my anxiety and I am eager to learn and strengthen my math skills. Thank you so very much!
@wackyLegends , You got it right !! That extra 0 comes as for 1004 the Base is 1000 ( it has 3 zeros thus 3 places to go )
@GothicDarkhellrazor 7x7=49. 7, 14, 21, 28, 35, 42, 49. So for 107, you have 7 more than 100 so you add 7, giving you 114. Then put 7^2 (49) on the end giving you 11449.
I think the easiest way to do this kind of thing is to use distributive property. separate 100 into (100+4). then you know it's 100^2 + 2*100*4 + 4^2, all of which are pretty simple to figure out and add together, especially since 100^2 =10,000 isn't hard to keep in your memory at all.
There's another video posted for #'s 30-70. Same idea, but your base# is 50 instead of 100. Find the distance of the # from 50 ie: 40. 40 is 10 less than 50 so subtract 10 from 25 (1/2 of 50) and that is your first 2 digits (15) then find the root of that distance 10^2 =100 ....so 00 are the last 2 digits the 1 gets added to the 2nd digit 5 making the answer 1600!
@ahmadguitar87 The principle is "Squaring a binomial"... It implies that ANY 2-or-more-digit number can be written as a binomial and squared in a realy simple manner...
Essentially we can break the problem down into the following:
104*104 = (100 + 4)^2
the general form of (a+b)^2 = a^2 + 2ab + b^2
We can factor so that we get (a+2b)*a + b^2
Now, in the first example, a=100, so we can take (100+8) and add two zeroes, to get 10800, and add 4^2 to get 10816.
Hope that this helped. I don't think that this method will work for >199, however maybe I missed something in the method used.
Good question !! Because it is the distance of Base that counts. 112 is at the distance of 12 ( not 2 ) from 100 . Shahryar
If it's an arithmetic sequence, then it can be expressed as a[n] = a[1] + (n-1)d, where a[1] is the initial term and d is the common difference. That said, we know that a[1]=16 and a[5]=17, so: 17 = 16 + 4d => d=1/4, and so we have the solution: a[n] = 16 + (n-1)/4.
@pinky93rocksm the reason you know that you have to add 2 additional digits, even if your starting under 100, is your equasion is being based off of the number 100. there are 2 additional digits after the primary, therefore you add 2 additional digits when you multiply. 2 x 2 = 4. just like if you went to use 1000 as a base instead, you would add an additional 3 digits. because 3 zeros. 3 x 3 = 6.
hope this was helpful XD
In Germany, we call this Referenzmethode. It's especially easy with squares, but it works not only with squares, but also with numbers which are not too far away from each other like 98 x 97 and which are near to an easy-to-calculate-with reference number, like 100 or 1000.
you can use the base 100:
1. subtract 13 from 87 => 74_ _
2. 13^2 = 169
3. add it to 74_ _ => 7569
It's because of the distributive law from elementary algebra. Do u remember high school, factoring quadratic equations? when you need to expand (4x - 5)^2 there was a shortcut instead of distributing, it's always
(ax + k)^2 = a^2*x^2 + 2*k*a^2*x + k^2
I don't expect u to remember, but the same rule applies when ur squaring a number
112^2 = (100 + 12)^2 = (100^2 + 2*100*12 + 12^2)
LOVE IT!!
Or you could
104 round to 100
104 - 100 = 3
104 + 4 = 108
100 x 108 + 4^2 =10816
This works with any number. Round to the nearest multiple of ten. Find difference. Subtract from original. Multiply two numbers. Add the difference squared.
@PlayerWaluigiii but you can only do the logarithm of a positive number so the answer -0.099=e^(x) can be eliminated. That leaves us with 10.099=e^(x) use logarithm to isolate x: x=[(log10.099)/(log(e^1))] x=2.31 I figured all of that out myself by the way. :)
why have stopped publishing the videos. All tricks are awesome. Please upload more
@PlayerWaluigiii e^(2x)-10e^(x)-1=0 let e^(x) become "x" to simplify things for now. This gives us (x^2)-10x-1=0 use quadratic equation to find that 2 possible answers are 10.099 or -0.099 these answers are our "x", which is really e^(x). So, 10.099=e^(x) or -0.099=e^(x) then use logarithms to isolate the real x. See next reply.
@EvilBharathy yes it works, 115 + 15 = 130, 100--> 2 zeros, so 2 numbers to go after 130. 15*15=225. since this number has 3 digits the first one is added to the last digit of the first number (so 130 becomes 132) and the 25 becomes after that, so it becomes 13225.
I hope I am explaining this the right way :)
Wish i had known these math tricks yrs ago!! I'll be able to use them. TY so very much!!
I would suggest you watch the 3rd easycal video on glad2teach website (link given below the video above) for a more 'spirited' explanation of using the Base. All the Best
Shahryar Badar Khan (Glad2teach)
Whether it is applicable for numbers above 100 ,ie for numbers like 201,254,648,555 ???
Thanks for making math so simple. I wish I knew these tricks in high school. You are great!!! Keep posting!!!
you're right by making 104 into 100+4
then you square that so you have a polynomial
(100+4)(100+4) then when you do polynomial multiplication you will end up adding 100000+400+400+16 which is the equivalence of adding 104+4 making it the first 3 digits and then adding 16 to the last 2 digits
It's very amazing easy way to calculate fast , thank you very much :)
glad2teach.. i really admire your math-tricks.. i am a mathstudent and since I learnd your tricks I can calculate faster than my professor :D
this is nice sir but i have a question !
incase to solve (124) whole square
according to u ,it will be 124 + 24 = 148 n then (24) square ...then how to solve (24) whole square as fast as u did
Having to bone up on my math. My son is going into AP this year and I'm afraid I won't be able to keep up / help him much longer. Thanks for the help!
Start by writing down 25 (five squared), and then consider the first digit (left to right), which is five, and then multiply it by the next consecutive natural number, which is six, therefore, 5 x 6 = 30. Placing these answers together gives: 3025. Hope this helps.
More sensible way, just rewrite as (a+b)^2 and apply expansion a^2 + 2ab + b^2
Sir i have confusion...after taking out 3 digits of square no. how do we know how may digits are left whether they are 2 or 3
ky eshte nje ushqim per truri.faleminderit
or you could use FOIL for all numbers (first outside inside last) for example, 104^2 = (100+4)(100+4) = (100)(100) + (100)(4) + (4)(100) + (4)(4) = 10816
I did it the binomial way, takes slightly longer (maybe 10sec instead of 5) but is just as easy: (104)² = (100 + 4)² = 100² + 2*4*100 + 4² = 10000 + 800 + 16 = 10816 or (96)² = (100 - 4)² = 100² - 2*4*100 + 4² = 10000 - 800 + 16 = 9216
@PlayerWaluigiii Easy. Follow along. Each step is separated by a space. [e^(x)-e^(-x)]/2=5 e^(x)-e^(-x)=10 e^(x)-[1/(e^(x))]-10=0 common denominator [(e^(2x)/(e^(x))]-[1/(e^(x))]-[((10)e^(x))/(e^(x))]=0 now eliminate denominators by multiplying the denominator on both sides of the equation. See my next reply (not enough room in this one).
73-27 is 46. So then you square 27 which is 729 and add it to the 46 (which needs two extra digits). So, add 729 to 4600 which makes 5329. This method is only really useful if the number is closer to 100 as the video says otherwise you get bigger number to square like 27.
that is a nice idea, glad2teach! But for the particular case of 55*55, won't it be easier to use 25*11*11, since there is a very easy way to multiply by 11?... like 275*11=3025, even if you don't know the *11 trick, you can even do 2750+275, which is easy 3025!... Of course, there are many ways to solve for sort of any calculation and I am just suggesting flexibility and to be one with the spark and the solution, if you know what I mean!...
If they teach they taught Math this way in the UK, kids would be so much better at it. :)
Thank you
You could improve the video and add it some depth with the general formula
(100+X)^2 = 10000 + 2*X*100 + X^2
As well as (100-X)^2 = 10000 - 2*X*100 + X^2
Digit separation works well when 0< X < 10
Btw, can you calculate 93*107 in five seconds? (100*100 - 7*7 = 9951)
It is equally simple if not simpler : (100+X)*(100-X) = 100*100 - X*X
This trick seems familiar(see "Be Human Calculator" video):
a^2 = 100*(a+a-100) + (a-100)^2
a^2 = 100*(2a-100) + (a-100)^2
a^2 = 200a - 10000 + a^2 - 200a + 10000
a^2 = a^2
seems like it'll always give the right answer.
For 2-digit numbers, instead of using bases as a means of calculation what do you feel about the technique ab^2 = (a^2) (b^2) (not multiplication simply placing the 2 answers alongside) + the sum of (a+b)x2
this is basically turning a number into : (100 + a)^2
so it becomes 100^2 + 200(a) + a^2
a very clever way to get these numbers quite quickly
You're videos are very helpful! Thank you for posting them! I wish I knew this stuff when I was in school so I would've had less homework and more play time! I am going to show your videos to my kids! Thanks again!
That is amazing. Sick method as well
You Sir, are amazing!
I have a maths exam tomorrow, I'm sure these methods will come in handy and save me lots of time!!
Thank you.
Thank you so much does these videos! I've showed them to everyone!!!
I REALLY LOVED IT. The numbers are so easy...Regards srabani from ASSAM, GUWAHATI
Thank you SO much for this. I'm in Algebra 2, and we're finishing chapter 6, which is polynomials.
GOD, this is going to help me on the test- she's not letting us use calculators on the first part.
YOU'RE MY HERO!
(Btw I think your accent is kinda cool :). Just for all those jerks who're being mean about it)
Thanks for taking the time to post.
This is helping me more than i get taught at school
Thanks for this video I am confuse in when mam teach the square but when I see your video clearly I explained thanks
Thanks for your kind advice !!
Shahryar (Glad2teach)
I have founded my own trick on squaring 1 - 110...And what a coincidence! It includes this trick also! It even works from 100 - 199
you use the term 'base' how do you know which base to use? what base would you use if the number ranges between 20-70?
you accent is awesome... idk why it just makes me smile hehehe
It's an Indian accent
I found one to share with you since you're so good at these.
you mean 3 digit numbesr? other 3 digit number are very easy too. If you mean 2 dgt no.s then, I can write it here: 34X34= 3x4x2(always two)so 3x4=12;x2=24, and add a zero (so 240) Second part: 3x3=9; 4x4=16; 9+16=916. Then add the first part to the second: 916+240=1156, 45x45: 4x5x20=400, 4x4+5x5=1625; 1625+400=2025, keep practicing :)
"Math is really simple, but we insist on making it complicated" Diego
Sir, You are lecturing me on the history which no one denies. I respect that. I'm stating the facts in present time. Why would Indians, Chinese, etc. want to come to the US and study? because the standards are far higher - conceptual education. No one who has studied in Subcontinent denies that schools put emphasis on rote learning - unless they are being dishonest.
55x55=50x60+25=3025
Generally, z5 x z5 = z0 x (z+1)0 + 25
Other examples: 35x35 = 30x40+25=1225; 85x85=80x90+25=7225
Enjoy! :)
hello glad2teach... please upload more videos... i love all your lessons...
had to think about that the whole time! Then i tried different examples and found out the trick behind it... You always have to multiply with the first figure of the base and then add wahtever the square of your "distance from the base" is...
Examples:
16^2 (base 10) --> 1*(16+6)=22_ ; 6^2=36 => answer: 256
24^2 (base 20) --> 2*(24+4)=56_ ; 4^2=16 => answer: 576
33^2 (base 30) --> 3*(33+3)=108_ ; 3^2=9 => answer: 1089
now you can go up to 99 and it will always work the same way!