The guy is amazing. These lessons brighten my day and let me recall all of my college years of math.
@420sakura1
Жыл бұрын
Yeah. All of them are basic maths but he's teaching them with no bells & whistle and straight to the point
@JennyWoo-vg1mu
Жыл бұрын
Thanks for teaching me. That"s is interesting process. Enjoy your every lesson again and again. This is NOT the answer I learn, but the PROCESS I truly enjoy it. So amazing !
@paultvshow
9 ай бұрын
What? Did you learn this in college? I learned this simple trick in middle school.
@dhwang101
9 ай бұрын
Yup you learn this in school and Fun story, this is how Richard Feynman beat the abbacus 😂
@alishozi1975
4 ай бұрын
8
@ComposedBySam
Жыл бұрын
For anyone wondering why this works, these are the first two terms of the binomial expansion.
@yousciencelab5307
Жыл бұрын
Of course. Ralph-Newton also works
@KYosco
Жыл бұрын
@@yousciencelab5307Newton-Raphson method
@victorpaesplinio2865
9 ай бұрын
Or the famous Taylor series of sqrt(x+h).
@Ennar
9 ай бұрын
This works because derivative is defined so it gives the best linear approximation: f(x) = f(a) + f'(a)(x-a) + o(x-a). In this particular case, sqrt(n^2+x) = n + x/(2n) + o(x).
@davicanto2899
9 ай бұрын
I have a better method: n=number s=closest perfect square number srqt(n) ≈ sqrt(s) * (3n+s)/(3s+n) Exemple: sqrt(138) ≈ sqrt(144) * (3*138 + 144)/(3*144+138) = 11.74736
@bt2gr8k72
Жыл бұрын
Bigger the number,it's relatively more difficult to find next number which is a perfect square. Also, error tolerance varies accordingly.
@IrrelevantGuy
11 ай бұрын
Yeah, that's a given. But this works great for figuring out the approximate value of smaller numbers, which will of course help you become faster at hand calculation (this is helpful especially for us Asians haha)
@MohamedBenamer940
10 ай бұрын
Use Halley method instead
@brodymiller9299
9 ай бұрын
At large numbers the second derivative of sqrt(x) is lower, so this becomes more accurate even if you don’t get the exact closest perfect square
@dhess34
7 ай бұрын
Thanks, Captain Obvious.
@JSSTyger
Жыл бұрын
I would like to offer a similar method. Let G = guess and E = error and we want to find the square root of C. C = (G+E)² = G²+2GE+E². With a small enough E value, E² will be close to zero. Our equation now becomes an approximation. C~G²+2GE and E~(C-G²)/(2G). Now that you have your approximate error, simply add it to G to get your final estimate. If you choose to get more accuracy, you can revise your guess. This method can also be extended to cube roots, etc by knowing the binomial expansion formula and eliminating the terms that have powers of E greater than 1.
@sussybaka6921
Жыл бұрын
Lol 🤣
@navamgarg
Жыл бұрын
Thankyou so much, you r in school, college or above?
@JSSTyger
Жыл бұрын
@@navamgarg I graduated with a minor in math in 2004. I took over 3 years worth of university math. But the funny thing is, I learned this on my own AFTER my schooling because I kept my old books. There was an interesting section on approximating square roots in my Numerical Methods book that never got covered and this was it.
@navamgarg
Жыл бұрын
@@JSSTyger Great, where are you from? And i guess you are 39 years old, is it right?
@JSSTyger
Жыл бұрын
@@navamgarg USA
@aaronaaron5013
Жыл бұрын
This is magnificent... the elegance of mathematics never stops marveling me.
@EEEEEEEE
10 ай бұрын
E
@aaronaaron5013
10 ай бұрын
@@EEEEEEEE EEE ?
@anneashley5110
8 ай бұрын
Buy the Trachtenberg book on mathematics. Devised by Polish mathematician whilst POW in Germany. Wrote theories on cigarette papers to stay sane. Escaped and eventually married rich Countess then dedicated his life teaching under privileged children easy ways of mathematics in academies in Switzerland.
@b.a.dieudonne4501
Жыл бұрын
Wow I started looking at your videos to keep my mind sharp. I am now forwarding them to my children. Amazing - you are a fantastic teacher thank you 🙏🏽
@mrhtutoring
Жыл бұрын
You are so kind
@gerrysecure5874
8 ай бұрын
Nope, he just says how to do it, not why it works. Draw 2 overlapping squares fixed at one corner, the correction are the 2 borders.
@asingh9540
7 ай бұрын
Me too.... hahaha 😅
@reigen-
Жыл бұрын
I like your teaching ❤🎉
@mrhtutoring
Жыл бұрын
Thank you! 😃
@kingminato5219
Жыл бұрын
We can use the tailor's series , f(x) = ✓x f'(x)= 1/✓x For each number we must find the perfect square a which is closer ( x > a) f(x) ~ f'(a) + 1/2 × 1/✓a × (x-a) f(138) ~ f(121) + 1/2 × 1/11 × 17 f(138) ~11,7 We get the first decimal of ✓x , for more precision check the tailor's series .
@michaelsibson7941
Жыл бұрын
Nice.
@olerask2457
Жыл бұрын
Nice, but f'(x) = 1/2 * 1/✓x. The first order Taylor approximation is f(x) ~ f(a) + f'(a) * (x-a). You do not need x>a, but when x is close to a the approximation is best.
@kingminato5219
Жыл бұрын
@@olerask2457 thank you for this fix
@marytredinnick3366
7 ай бұрын
Im 60 and have BS in Elementary and Special Education.Now that Im retired I'm enjoying learning algebra. I soooo wish i could have had you as a teacher. You're so good at explaining each step. Thanks so much❤
@yvesdelombaerde5909
6 ай бұрын
Then iterate. Newton-Raphson algoritm. You can generalize to nth root. If a is an approximation and e stands for error then Sqrt(x)=a+e squaring both sides x=(a+e)²=a²+2ae+e² Assuming e is small wrt a: x~a²+2ae e~(x-a²)/2a Replace e, get a better approximation and iterate.
@victorpaesplinio2865
9 ай бұрын
This is the first order Taylor expansion of sqrt(x+h). It gives better results smaller the h, unless you go a bit further and add a second order correction √(x+h) = √x + h/(2√x) - h²/(8h^(3/2)) + O(h³)
@pattyguy
3 ай бұрын
are you casting spells on us
@stephenhousman6975
9 ай бұрын
To those of you taking calculus this approximation is a first order Taylor series for the square root of x.
@olerask2457
Жыл бұрын
In general f(x) ~ f(a) + f'(a) * (x-a). That is 1. sqrt(x) ~ sqrt(a) + (x-a)/(2*sqrt(a)) 2. cuberoot(x) ~ cuberoot(a) + (x-a)/(3*(cuberoot(a))^2), etc. Fx. cuberoot(75) ~ cuberoot(64) + (75-64)/(3*(cuberoot(64))^2) = 4 + 11/(3*4^2) ~ 4.2292, where cuberoot(75) ~ 4.2172.
@MyAmygdala_
Жыл бұрын
Thank you 😊
@mrydobon
10 ай бұрын
I think you have to show this Taylor series expansion if you want to teach this approximate solution to a square root. Otherwise it is better to just teach the linear interpolation solution, which is intuitive just by looking at the number line. It is not as accurate, but it doesn't require any calculus to understand. And we're talkin about approximate solutions either way. In this example, 12 + (138-144)/(144-121) = 11.74. That's still a pretty good approximation.
@niggydiggy3992
8 ай бұрын
I dont speak mincraft enchanting table
@YourAveragePlay3r
7 ай бұрын
Really appreciate this guy popping up on my feed once a day, extremely helpful.
@Martini16REAL
9 ай бұрын
This is the coolest thing ever. I have tried to figure out how to find an approximation of a square root and now I can.
@honeyartstudios
Жыл бұрын
These daily clips might help me overcome my math trauma
@thalesnemo2841
Жыл бұрын
So straight forward and simple ! My recollections are that the textbook method was too complex !
@alpcetinkaya3656
Жыл бұрын
It is between the distance 121 to 144, which is 23. 138-144 = -6. Then -6/23 ~ 0.26. Then 12 -0.26= 11.74. It can be calculated from 121 also.
@Daniel31216
Жыл бұрын
That's because he's used the Taylor series, which approximates a function about some point. The function he used, which I'll call f(x), is given by: f(x) = √x To find an approximation, fist you need to pick a point on the original function. Because we want to approximate f(138), it makes sense to pick the closest number to 138, that is also a perfect square. 144 is the closest perfect square, but you can use numbers a little further away. It's hard to explain it here, so it might help to look up "Taylor Series 3blue 1brown" to get a more visual look at it.
@roywimar
Жыл бұрын
I use calculator for result -6/23😊
@alpcetinkaya3656
Жыл бұрын
@@roywimar 😀 I would use calculator for sqrt(138). But to do it mentally or to approximate, i think it is easy to approximate -6/23 ~ -6/24 which is 0.25
@gamerpedia1535
Жыл бұрын
@@Daniel31216 this is actually just propagated error.
@mitchellhayman381
Жыл бұрын
No shit Sherlock
@brettkowalski
9 ай бұрын
This guy is bringing back my migraines I used to have when I was doing math competitions in middle school and high school.
@ChrisM541
7 ай бұрын
Very well explained. If only we all remember that we can use this 'way of thinking' in many, many more cases in our lives.
@kevintarrant5854
4 ай бұрын
I was wondering the same thing, but can you actually name one. ?
@MikolaZak
8 ай бұрын
Я не розумію мову викладача, але він так добре пояснює, що інтуїтивно зрозуміло все. Дуже добрий викладач!
@anuragswain5910
8 ай бұрын
Just wow 😍.....Quite amazed by your simplified teaching style sir..... Please keep us guiding through the gigantic universe of Maths
@mrhtutoring
8 ай бұрын
Thank you for the nice comment!
@predatorff8274
Жыл бұрын
f(a+h)= f(a)+h. f'(a+h) use derivatives and consider f(a) as perfect square which is closest to 138 and it's done ; a=144, h=-6
@Kelsey-qh7rh
2 ай бұрын
You taught this WAYYY better than my online math lessons
@rinkudamanrd
6 ай бұрын
ah. this is basically using the derivative to make a tangent line approximation simplifed! nice video!
@krishnagarg1313
Жыл бұрын
Thank you sir for such helpful tricks😊😊
@nowonwoo9528
8 ай бұрын
There's also one easier method to do this that almost yields the same results, albeit the margin of error is higher than this method. For the sqrt(138), find the closest smaller square root, which is 11. And then find the difference between the perfect square and the number; hence, giving us 17. Make a fraction and put the difference on the numerator while twice the square root is the denominator, giving us 22. This would yield to a mixed fraction of 11 and 17/22, or 11.77
@BBalasa
4 ай бұрын
Wow , great universal solution.. Thank you..
@billjohnson3858
5 ай бұрын
Linear interpolation is easier to remember and just about as close. Since 144-121=23 and 138-121=17 so 17/23 gives us 0.739 which is the fractional part of 11.739
@user-oz4ph6zl8h
7 ай бұрын
شكراً لك. شرح جميل أعاد لنا الذكريات القديمة في المدرسة
@vaishnavisardar
Жыл бұрын
Just do thia :- if you want to find the square of 95 :-do 5 square write one no and carry second then do 9 square and double up the value and add the carried no.
@yuridxh
9 ай бұрын
You can do like this too: 11
@vibushithirthankar
7 ай бұрын
Thank you sir❤.. this is very helpful 🙏🏻
@jmolvera8337
8 ай бұрын
Super, I will memorize this procedure! Thank you professor!
@villageidiot2372
9 ай бұрын
Love these lessons, great explanations.
@kaichousan8626
6 ай бұрын
This is just the best method, instead of doing the hard stepdown like approach
@murdock5537
10 ай бұрын
Simply great, many thanks, Sir! 138 = (12 - x)^2 ≈ 144 - 24x → x = 12 - 1/4 = 11,75 (don't use x^2, it's very small btw)
@AftabAlam-yw4eq
9 ай бұрын
The method we learned was If you want to find square root of X. The it will be (X+Y)/(2.Z) Y is the nearest perfect square and Z is the square root of Y. Which is a more simplifide form of this equation.
@mineapple1165
Жыл бұрын
This is actually really useful because sometimes i forget my calculator at home and everyone in my class doesn't want me to use the one they own Thank you sir
@mrhtutoring
Жыл бұрын
Very happy to hear that it's useful 😀
@stonetee1845
Жыл бұрын
you are indeed a maths genius. pls where do you get these shortcuts from. it's just incredible. wow
@NicholasOfAutrecourt
Жыл бұрын
It's a derivation from differential calculus.
@stonetee1845
Жыл бұрын
Okay, l see
@stonetee1845
Жыл бұрын
Thanks
@Daniel31216
Жыл бұрын
He used the first two terms of the Taylor series. It's not normally used for stuff like this, but the series can be used to approximate any function you want.
@yaksh_patel
Жыл бұрын
You can also do it as: (138/12 +12)/2 = 11.75 First divide 138 by 12 and add 12 to the answer then divide the answer you got after addition by 2 and you will get approximate answer.
finally ! thank you ! I've been doing bad approximations all my life !!!
@kumarumang4127
8 ай бұрын
this is the derivation from (a+b)^2 expression
@maxwiebe357
7 ай бұрын
for a rougher but quicker one, take the lower of the 2 close roots (121), take that as your whole number, multiply it by 2 and that’s your denominator, find the difference of your original and the perfect square and that’s your numerator 11 and 17/22 = around 11.71
@yvesdelombaerde5909
6 ай бұрын
For 3th root, do the same with the 1st term of (a+e)³ dropping the e² and e³ terms etc.
@FreeOnlineSchoolBD
8 ай бұрын
Those who are wondering how does this method work. This is newton raphson method, it converges easily and a part of numerical calculation.
@sarabana3093
Жыл бұрын
Nice. My Math's teacher from Iran called this method "BANNA" in Persian which is very use full at Entrance Exam
@luisclementeortegasegovia8603
Жыл бұрын
Excelent 👍 Beautiful algorithm.
@mrhtutoring
Жыл бұрын
Many thanks!
@asseroy
8 ай бұрын
L(x)=f(a)+f'(a)(x-a) where a is the closest perfect square to the number we're trying to approximate (a=144) L(x)=√(144)+(1/2√144)(x-144) L(138)=√(144)+(1/2√144)(138-144) =12+(1/2×12)(-6)=12-1/4=11.75 √(138)≈L(138)=11.75
@jpo3811
6 ай бұрын
Multiple succinct high quality demonstrations.
@ronaldbell7429
Жыл бұрын
I'd be interested to see how that equation was derived, to be honest
@yousciencelab5307
Жыл бұрын
Ralph-Newton iteration gives you this. Let √N = x N = x² N - x² = 0 f¹(x) = -2x x₁ = x₀ + f(x)/f¹(x) For this case, N = 138, x₀ = 11 or 12, which ever you want to start from. x₁ = 11 - [138 - 11²/(-2 × 11)] x₁ = 11 - [138 - 121/(-22)] x₁ = 11 - [17/(-22)] x₁ = 11 + 0.77 ≈ 11.77 Binomial expansion can also be used
@aashutoshgoswami344
11 ай бұрын
It is derived using the derivative of √x Which is 1/(2√x)
@blurr1903
10 ай бұрын
It’s newtons approximation formula of f(a)+f’(a)(x-a)
@floris2042
9 ай бұрын
its the first order taylor expansion of the square root
@WildayMATH
Жыл бұрын
thanks Prof for the bright explained
@vishalgamer710
10 ай бұрын
It's is also mentioned in vedic maths...
@RivaldoDaviero-dc2vx
14 күн бұрын
This is really helpful wow😮
@aku7598
Жыл бұрын
Approximation by differentials.
@carolinehammes
Жыл бұрын
Excellent!
@leeFbeatz
8 ай бұрын
Thank you!!!!! 🙏
@shivanshnigam4015
Жыл бұрын
you can generalize this for any kth root of a number by using binomial theorem
@mrhtutoring
Жыл бұрын
Good observation 👍
@marc-bs8bj
Жыл бұрын
Excellent estimation method!!
@deanmoncaster
8 ай бұрын
Wouldn't it just be easier to take 138 from 144 then take that result from the root rather than adding a negative which most people can't do.
@mrhtutoring
8 ай бұрын
Yes, certainly. I did post another shorts video on the method you commented.
@ionescunicolae473
10 ай бұрын
Amazing ! Thank you very much.
@AshwaniMaurya-ph3vs
8 ай бұрын
Also can be calculated using derivative method
@grantgautney7900
9 ай бұрын
The tapping sound of chalk on a black board takes me back.
@omshinde5064
Жыл бұрын
Concept in chapter Application of derivatives
@javierjones6682
5 ай бұрын
Great video sir
@DeepanshuGupta-gl2sm
4 ай бұрын
* THIS TRICK IS BEST WHEN NUMBER IS SMALLER THAN THE CLOSEST PERFECT SQUARE *
@TechnocratSohail
Жыл бұрын
Very nice..It is quite useful..
@mrhtutoring
Жыл бұрын
Thanks a lot
@erikblaas5826
9 ай бұрын
I have learned it another way... The part of writing it down is more complicated, but there is hardly making square root calculating in it.. mostly devisions and adding or substracting...
@Sg190th
Жыл бұрын
I like this. Much simpler than using the Newton method
@markyujoco1912
Жыл бұрын
That is also Newton's method, he was just clarrifying it hahhaahah ....... 😅😅😅😅😅
@michaelsibson7941
Жыл бұрын
Careful bout how you talk bout newton.
@MathTidbits
Жыл бұрын
@@michaelsibson7941 newton gonna sue you ?
@cruelfish4824
10 ай бұрын
Oh? I did something similar. I took 12^2 = 144, asked myself what % of 144 is 138, roughly 0.96%, took away half of that 4% diff from 12, giving me 0.98% of 12 or roughly 11.76. No clue if it works for all numbers or even any number but I tried.
@AL.BUNDY.
7 ай бұрын
0:56 I like it
@vimax3858
Жыл бұрын
I remember when I was in 4th grade and questioned a teacher how to solve roots that are irrational numbers and they had no clue, now KZitem gives it to me.
@peterirvin7121
11 ай бұрын
It's very sad that math literacy is not required to teach elementary school.
@rekkoha-dk1nh
7 ай бұрын
Thanks, Mr. H.
@fifthavenue8505
7 ай бұрын
Thank you!
@equinoxxx5453
Жыл бұрын
can anyone tell me what kind of board is that and how much does it cost :)
@KeoniPhoenix
Жыл бұрын
That's a standard blackboard or chalkboard with a projector projecting the white text to it. Its actually useable in most instances because the black surface isn't a very good black color and allows the light being shined on it to bounce off of it creating the visible image of the square root of 138 and the number line.
@Beginning497
Жыл бұрын
😂got the point😂😂
@taciodasilva8291
9 ай бұрын
There is a 12 years old girl in Bradil that is famous because she developed a method to calculate the square roots where the roots are integer numbers. I belive, now, by coincidence or not, this is the same method, just simplified in her case.
@nekoya15
6 ай бұрын
√x ≈ √y + (x - y)/2√y Where x is not a perfect square and y is the perfect square nearest to x.
@stevenmiller5999
9 ай бұрын
That was absolutely awesome thank you
@mrhtutoring
9 ай бұрын
Glad you enjoyed it
@obinnanwakwue5735
8 ай бұрын
Straight outta differentials! Let y = sqrt(x), then dy/dx = 1/(2*sqrt(x)), so dy = (1/(2*sqrt(x))*dx. dy can be approximated as y - y0 and dx as x - x0, giving us y - y0 = (x - x0)/(2*sqrt(x)) or y = y0 + (x - x0)/(2*sqrt(x)). Here he used (144, 12) as (x0, y0), so y = 12 + (138-144)/(2*sqrt(144)) = 12 - 1/4 = 47/4 = 11.75.
@christianmosquera9044
9 ай бұрын
Excelente vídeo maravilloso 😊😊😊😊❤❤❤❤❤
@mrhtutoring
9 ай бұрын
Gracias~🙏
@nth.education
8 ай бұрын
Amazing!
@evilsensei8262
7 ай бұрын
Bold of you to assume I know how to do fractions 😅. Awesome video!
@mrhtutoring
7 ай бұрын
Thanks! 😃
@AmarDas-wg2sq
Жыл бұрын
You are phenomenal Is there any couses you provide
@mrhtutoring
Жыл бұрын
Not at this time~
@jwlee654
7 ай бұрын
Awesome. I am not even in a math intensive job or course of study, but I will definitely use this!
@ionbintf
7 ай бұрын
"Pretty DARN close"...
@foff9275
4 ай бұрын
Brilliant. Gracias
@rohitpandey-ce9lg
Жыл бұрын
Newton raphson method. Numerical analysis method.
@n.gineer8102
9 ай бұрын
If I recall this technique was used by Hans Bethe as described by Richard Feynman the part of his book about working on the Manhattan Project.
@blurr1903
10 ай бұрын
So basically just f(a)+f’(a)(x-a) where f(x)=sqrtx, a = 144 and x= 138 so sqrt144+ (1/2(sqrt(144))(138-144) or 12+ (1/24)(-6) or 12-(1/4) = 11.75
@tommymyers3183
Жыл бұрын
You make it look easy.
@velmurugank4871
7 ай бұрын
If I had a math teacher like you back in school, I would have scored better in my Maths exams.
@KissMan-lz7ej
7 ай бұрын
Thank you so much, sir
@quandarkumtanglehairs4743
Жыл бұрын
Love it! Very useful, thank you. Another tool in my box of...tools. I have other boxes, not just of tools, I guess is what I'm saying.
@mrhtutoring
Жыл бұрын
Glad it was helpful!
@nikoladrakulic5577
9 ай бұрын
x=138 and y=144 sqrt(y)=12 sqrt(x)=(x+y)/(2*(sqrt(y))) =(138+144)/(2*(sqrt(144))) =282/(2*12) =11.75
@ART7N23
Жыл бұрын
Sensai ur awesome 😫😫🙌🏻🙌🏻🙌🏻
@BeeeHonest
7 ай бұрын
Brilliant!
@aimranehd
8 ай бұрын
this is really handy! especially because i have a national math exam at the end of this year, and one of the subjects that will be included in the exam are roots, on top of that they dont allow calculators. thank you so much, mrhtutoring!
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