Next time my math teacher says my answer is wrong I'll say, "but it was pretty darn close"
@MartisGTR
Жыл бұрын
HAHAHAHAHAHAHAHA
@Clda47
Жыл бұрын
Is approximate answer
@PsyQoBoy
Жыл бұрын
Technically he's right if it's to 1 d.p
@VW.907
Жыл бұрын
Haha
@vibeslide
Жыл бұрын
My thoughts exactly. Mathematics as it is taught in school is about precision not approximations, regardless of how cool they are. One of the reasons i hated it.
@mrhtutoring
Жыл бұрын
After making the video, I realized I used the = sign by mistake. I meant to say the approximate square root of 102 to square root of 100.
@ummerfarooq5383
Жыл бұрын
Did you invent this method?
@ummerfarooq5383
Жыл бұрын
@@mrhtutoring UCLA invented it?
@ishanshah230889
Жыл бұрын
It is 102^(1/2) =(100+2)^(1/2) =[100*(1+2/100)]^(1/2) =100^(1/2)*(1+2/100)^(1/2) =10*[1+(1/2)*2/100±...] (Maclaurin series, ignore higher order terms as they tend to 0) ≈10*(1±0.01) ≈10.1
@mrhtutoring
Жыл бұрын
@@ishanshah230889 I appreciate it. Thank you.
@fillfreakin2245
Жыл бұрын
It seems needlessly complicated. Why say it's approximately equal to 10 + 2/(2*10)? The remainder "2" will always cancel out if you put it on the numerator and the denominator. Easier to say it's about 10 + 1/10.
@tolbryntheix4135
5 ай бұрын
For those who want to know, this is an application of the newton method, which allows you to find the root of a nonlinear function very quickly (Each iteration roughly doubles the amount of digits that are accurate). In this case, the function with root sqrt(102) is f(x)=(x^2) - 102. In the Newton Method, you pick a starting point x_{0} and get a better approximation of the function's root by inductively defining x_{n+1} = x_{n} - (f(x_{n})/f'(x_{n})) In this case, we apply 1 iteration with x_{0} equal to the smallest whole-numbered root smaller than sqrt(102), which gets us close enough to the real root for the newton method to substantially improve the guess. We can check that the equation used in the video is the same by plugging in the values: x_{1} = x_{0} - (f(x_{0})/f'(x_{0})) = 10 - (-2/2*10) = 10.1 The newton method works pretty generally with differentiable functions (careful: its bad if the root is also a stationary point, it can be adjusted to rectify this flaw though) because the geometric intuition is that it puts a tangent line on the starting point and computes the intersection with the zero line, which is really close to the functions intersection with the zero line (its root) if the starting point is already close to the root of the function. See Newton Method on wikipedia for a nice graphic showing this concept.
@flyergaming3019
4 ай бұрын
I understand but didn't understand 😂
@guddikhatoon1965
3 ай бұрын
Me too😅
@telemans107
3 ай бұрын
Isn t this a Taylor expansion approximation ?? Using only the first derivative ??
@tolbryntheix4135
3 ай бұрын
@@telemans107 yes, you can look at this using just first digit Taylor approximation: the important thing is that the error of the Taylor series gets small very quickly in almost all cases when the current value is close to the root of the function, which allows this method to converge.
@telemans107
3 ай бұрын
@@tolbryntheix4135 Thank you .I have stadied that 40 years ago in Rabat Morocco but still in touch.
@victoriaspade
Жыл бұрын
Doing math on the chalk board. Miss those days❤
@invincibleghost__23
8 ай бұрын
R u Indian?
@joorguy
7 ай бұрын
we still use it
@blueshot333
4 ай бұрын
You talking as if we do maths on telebooks 😂
@SS_1_great
3 ай бұрын
that is racist@@invincibleghost__23
@NaveenB-ov1jy
Ай бұрын
@@blueshot333well most schools use whiteboards and now BenQ screens
@ryanolsen13
Жыл бұрын
Never seen a math teacher accept “pretty darn close”
@herman7880
Жыл бұрын
You should try an advanced mathematic course, theres ton of numerical estimations for unsolveable equations. Its called numerical estimation. But usually you can increase number of iterations and can get an accuracy as accurate as possible, down to 10**(-(15+)) if you want.
@h4m1d39
9 ай бұрын
@@herman7880Which will be pretty darn close
@Ninvus2
8 ай бұрын
Pretty darn close is the entire idea behind limits in calculus
@plumjet0930
8 ай бұрын
Mine did In 4th grade she didn’t accept me putting 0.33 for 1/3 but accepted 0.35 for 1/3
@jffrysith4365
8 ай бұрын
@@h4m1d39 to be fair, if you took the taylor series to finity, you would be 0 of. That's pretty darn close if you ask me!
@hongminh4963
Жыл бұрын
Ok now let me introduce Taylor's series...
@joj0ee
Жыл бұрын
Don’t need a series, just do linear approximation
@EliteCubingAlliance
Жыл бұрын
@@joj0ee But Taylor series is more accurate
@livef0rever_147
Жыл бұрын
Newtons method is far superior than taylor series for approximating numerical roots
@random19911004
Жыл бұрын
taylor series is a generalisation. If you take the constant and linear term of taylor series, it is linear approximating. All this video uses is f(x+h) = f(x) + h* f '(x) where f'(x) = 1/(2sqrt(x)) , x = 100 and h = 2
@davidnewman8629
Жыл бұрын
😂
@sobhitkumar7250
Жыл бұрын
"Let me teach you some Calculus without Scaring you away-"
@sirdragrimverma777
10 ай бұрын
Exactly
@thailandler1110
8 ай бұрын
I want to learn then😁😊
@carultch
7 ай бұрын
@@thailandler1110 Here's how it works: Given y = sqrt(x) Approximate this function near the nearest perfect square, at x=100, with a tangent line that touches it and locally matches its direction. The point slope form of a line is: y = m*(x - x0) + y0 x0 = 100, and y0 = 10. All that's left to find is m, the slope of the tangent line, dy/dx. y = sqrt(x) = x^(1/2) If y=x^n, then dy/dx = n*x^(n - 1), which means: dy/dx = 1/2*x^(1/2 - 1), which can be rewritten as: dy/dx = sqrt(x)/(2*x) Evaluate this at x=100: m = dy/dx = sqrt(100)/(2*100) = 10/200 = 1/20 Thus, the tangent line is: y = 1/20*(x - 100) + 10 Plug in x=102: y = 1/20*(102 - 100) + 10 Result: y = 10.1
@purplevanilla
5 ай бұрын
Thats how to teach students about math. Make it simple and clear, not terrifying and complex.
@Bobsmith-yf9oy
2 ай бұрын
Not in my lifetime! Been there, tried that.
@MyAmygdala_
10 ай бұрын
Wow I've been searching for an easy method to find square root but no one said like this.......this is very very easy..! I tried for √109 and I got 10.45 as approximate value and the correct value is 10.4403...... I'm going to send this to all my frnds who r struggling Thank you soooo much ❤❤
@mrhtutoring
10 ай бұрын
Happy to help
@ubuandeyelbme
Жыл бұрын
It should be noted that the 2 in the denominator is NOT the same 2 as in the numerator. The denominator 2 is a constant and is always used regardless of the remainder from the number to be square rooted and the closest perfect square.
@coromknight3171
Жыл бұрын
Thx. I was wondering about that.
@Gottenhimfella
Жыл бұрын
It was the least clear part of the demo, in my opinion too.
@tatesmith4527
Жыл бұрын
That was REALLY confusing and not clear in the video ! Thank you !
@ubuandeyelbme
Жыл бұрын
@@Gottenhimfella I was thoroughly confused at first lol
@1michiganbuck
Жыл бұрын
Thank you. I was running some other numbers and didn't get even close, but your comments helped to clear it up.
@misterrhombus
Жыл бұрын
For those that want to learn more. This is called Local Linear Approximation
@virulenceconviction5343
Жыл бұрын
Thank you
@mandarbamane4268
Жыл бұрын
Or approximation using first principle of derivative. f(x+h) = f(x) + f'(x)/h (h is very small) Also (sqrt(x))' = 1/(2*sqrt(x)) That's why there's "2".
@connieb3694
Жыл бұрын
Thank you
@DevineAbyss
Жыл бұрын
It is also horribly unprecise and there is no need to actually use it. You can actually do it from both sides: sqrt(102)=sqrt(100+02)=sqrt(10*10+02) ~10+02/(2*10)=10+2/20=10,1 sqrt(102)=sqrt(121- 19)=sqrt(11*11- 19) ~11 -19/(2*11)=11-19/22~10.136 The further you are away from the the actual squared number (100 or 121) the wronger it gets. 102 is really close to 100, which is why the result is somewhat good. You could technically also do something stupid like picking a square that is not adjacent and get something horribly wrong (: sqrt(102)=sqrt(49+53)=sqrt(7*7+53) ~7+53/(2*7)=10+53/14~10,79 I approcimated 102 with 49, which is 7*7 (:
@manansharma9164
8 ай бұрын
It is called Binomial Approximation. (1+x)^n is approximately 1+nx if x is very small as compared to 1.
@mryashoo2218
6 ай бұрын
I solved All Kinds of Equations in School And College. Now I am Security Guard and my Salary gets "Square Root" on a very first day 😭😭😭
@KamiXTwelve
7 ай бұрын
I Wasnt Even Paying Attention To What He Was Doing Because I Was Just Imagining How SMOOTH It Sounds When He Writes With The Chalk
@mariatorres9789
5 ай бұрын
Oh, you're one of *those* people. I always paid attention. Shrugs
@charkenespleeta
5 ай бұрын
@@mariatorres9789 What’s wrong with listening to chalk sounds? its a yt short anyway, it’ll replay
@ryan.y4895
Жыл бұрын
Somehow, the chalk hitting the board sounds satisfying
@johns_craft8582
Жыл бұрын
Ik
@johnonduku5922
Жыл бұрын
asmr
@mrhtutoring
Жыл бұрын
It helps with concentration as well.
@arpieravidas7731
Жыл бұрын
I hated it. Felt like someone is banging my front door during a hangover.
@NatarajSubramanian
Жыл бұрын
Yeah brings back some good memories of learning in school. 😊
@Michaelmouse23
Жыл бұрын
He's like Bob Ross of maths. I thought he was going to say we're going to put a happy little number justttt here at one stage.
@lauragraves4342
Жыл бұрын
Square roots do make some happy little trees.
@IKAA-6
Жыл бұрын
😂😂
@azrasadia8449
9 ай бұрын
Gfc
@mrjodoe
7 ай бұрын
what is Bob Ross?
@sj-comps
7 ай бұрын
@@mrjodoea really cool drawer
@waltervetri2476
Ай бұрын
Thank you for the lesson ,Sir .Learning every day .Vetri South Africa 🙏🇿🇦🙏
@criticalthinker9134
4 ай бұрын
It's just the zeroth iteration of Newton ralphson method. 😅
@jacksonsmith2955
2 ай бұрын
Yup! They both function via a linear approximation.
@noa4953
Жыл бұрын
for anyone wondering this is actually the beginning of the Taylor series of the square root function (around the closest perfect square, 100 here). The next term in the sum (for more accuracy) would be -(x-a)²/(8a sqrt(a)) with "a" being the perfect square. Here (x=102, a=100) it would give 10 + 2/(2*10) - 2²/(8*100*10)=10.0995 (exact value)
@copculerkral1157
Жыл бұрын
what is a and x in your formula?If a=2 then it would be in your formula: 2²/(8x2x2²).So if you say a=10 then in your formula:10²/(8x10x10²). This is what I understood from your formula.Can you make it clear please?
@lipcseisandor5342
Жыл бұрын
@@copculerkral1157 The number of which you take the square root is x and the closest approximation you use is a. So in this case x = 102 and a = 100. The sum of the first two terms in the Taylor Series is f(a) + f'(a)/1! * (x-a). Since f(x) is sqrt(x) in our case, you get the result.
@awvz_1194
Жыл бұрын
That is not the exact answer, the exact answer is √102 or the infinite Taylor expansion
@lipcseisandor5342
Жыл бұрын
@@awvz_1194 Yeah :)
@noa4953
Жыл бұрын
@@awvz_1194 Yep, what i was trying to say is that this value is the exact result of the sum i wrote (the first 3 terms)
@LTV_inc
Жыл бұрын
Nice! As a retired engineer i think more people need to learn algebra, not to master it but to learn a different way of thinking about numbers.
@ApesAmongUs
Жыл бұрын
But this does none of that. It's a set of instructions to get an approximate answer. To show different ways of thinking about numbers, he would need to show why it works - or better yet, walk the viewer through the thought process for figuring out the trick.
@painting
Жыл бұрын
Nah, I'll just remember Arbitrary rules and tricks.
@Frandahab
Жыл бұрын
This isnt algebra
@adityakamat9856
Жыл бұрын
@@ApesAmongUs This trick is based on binomial approximation.
@ApesAmongUs
Жыл бұрын
@@adityakamat9856 You just dropped jargon. Doing that does not help anyone "to learn a different way of thinking about numbers". Also, the fact that you thought you were telling me something I didn't already know tells me that you did not understand my point.
@Aman-sw9lw
Жыл бұрын
Really good trick this would really help me in my exams as calculators are not allowed. Thank you again sir
@mrhtutoring
Жыл бұрын
Always to happy to hear that it gets used.
@ArtemisShanks
Жыл бұрын
This guy is so great for doing this on yt. Say what you want about the normal stuff, but this kind of universal teaching is invaluable.
@uhighsmith
Жыл бұрын
I’m fifty years old and through out my years I’ve had trouble with math. I’ve had several teachers over the few years I was in school and they all seemed to rush through the process. I really enjoyed this video and will be watching more. Thanks for your sharing and time.
@maryapatterson
Ай бұрын
What is good learning on YT is that you can replay until you get it!😂
@RexVelde
Жыл бұрын
For anyone who are interested in this algorithm, this an application of newtons method iterated once. Netwons method is a way to approximate a value x such that f(x) = 0. In order to make such a function we make it be 0 when x is correct: f(x) = n-x^2 x ≈ guess - f(guess)/f'(guess) Repeat with the new guess being the current x. This works for many other cases as well, i.e. third root: f(x) = n - x^3 x ≈ guess - (n-guess^3)/(-3*guess^2) A little more complicated, but still highly doable.
@bolomniejaja
Жыл бұрын
Thank you for that explanation❤
@IhsanMujdeci
Жыл бұрын
They used this trick in the first quake game I believe. But they also used other tricky bit wise logic as well. This was used to normalize a vector I think for light calculation.
@RexVelde
Жыл бұрын
@@IhsanMujdeci that makes sense, as a lot of calculators also use this algorithm with more iterations and a look up table.
@bertbaker7067
Жыл бұрын
I was having flashbacks of newton's method but wasn't sure glad i was remembering in the right direction
@bubs5278
Жыл бұрын
What is the real world application for square roots?
@Kingboo_17
4 ай бұрын
I like how passionate and smart teachers like you say "Pretty darn close" or "close enough" while teachers who just reads and gives an example are often the one's that says everything has to be precise. Kind of crazy lmao
And this RIGHT HERE is why I ALWAYS carry my calculator at all times with me.
@boomblast2786
Жыл бұрын
Dude smart devices 😅
@clarenceratkowiak7287
Жыл бұрын
What?
@StephenButlerOne
Жыл бұрын
It's called a phone
@mittelwelle_531_khz
Жыл бұрын
Is this another way of saying: Without my calculator I feel helpless? In retrospect I wonder how we people born up to the early 1960s (so joining the school system up to 1970 - as electronic calculators dropped into an affordable range during the first half of the 1970 decade only) could cope with calculating anything beyond simple addition, subtraction and multiplication (say up to 20×20).
@EyeLean5280
Жыл бұрын
I worked at an inner-city school where the math teacher didn't believe the kids could learn (of course they could). He gave them calculators for the simplest things, thus making sure they DIDN'T learn. That's what you're doing to yourself.
@hexagon8899
Жыл бұрын
the larger the number is the more precise this gets
@Inferno.522
Жыл бұрын
accurate*. The larger the number, the more accurate this method gets.
@jo54763
Жыл бұрын
@@Inferno.522 The better you are at preventibg mistakes, the more precise this gets 🤣 EDIT: Case in point, just gonna leave it there
@cherryzzz6229
Жыл бұрын
@@jo54763 I don't get why we'd use this method? I'd just find the largest root numbers of each then simplify it until I get the smallest surd. Kinda useless in my opinion.
@jo54763
Жыл бұрын
@CherryZzz I wasn't commenting on the method, just adding to the accuracy vs precision statement.
@Ennar
Жыл бұрын
@@cherryzzz6229 how do you think calculators work? Pulling digits out of a magic hat?
@captainhaire
2 ай бұрын
I get the feeling this guy is shredded.
@ebrahimkhalili4967
8 ай бұрын
For more precision, you can add more terms of the taylor series of square root function
@awvz_1194
Жыл бұрын
Like others have said, it's just the first two terms of the Taylor expansion, but for the love of God, please don't abuse the equals sign like that
@debunkthis
Жыл бұрын
Guys I found the mathematician.
@arcanine_enjoyer
Жыл бұрын
Abuse the equals sign? How the hell do you do that?
@Jechew
Жыл бұрын
@@arcanine_enjoyer he wrote an untrue statement using equal sign
@S20171
Жыл бұрын
@@arcanine_enjoyer he wrote √102=√100
@user-bs4qu7tb2g
Жыл бұрын
@@arcanine_enjoyer I don't even like math that much, but seeing how he wrote root(102) = root(100) was so painful to watch, it really made my brain hurt for a bit.
@williamroncallo7926
Жыл бұрын
This was my typical math teacher, growing up in the 70s, never teaching anything about why, so I just memorized.
@zfloz9895
Жыл бұрын
You are absolutely correct!!!
@CS-et4fs
Жыл бұрын
Can’t teach a “why” into a 1minutes video. If u want to know a “why”. Search up “taylor series” and see how is it going. The reason most low level math class in middle school etc doesn’t teach into the detail is because the detail is so complicate and unnecessary when trying to solve the real world problem. No one is using definition of derivatives all the time to solve basic polynomial. They just memorize the rule. But once get used to it, it may be a great idea to come back and see how it work under the hood. This is good because not everyone is interest in math, it would be overkill to go into detail for everything about math. It should be left for passionate students to learn it by themselve. People that are nớt interested in math can just use the short cut method for their daily life
@turtle_combat
Жыл бұрын
It's a goddamn KZitem short.
@XRioteerXBoyX
Жыл бұрын
Thank you professor for accepting the answer when it is "pretty darn close".
@ivanderpanguene5189
11 ай бұрын
Thanks sir, now I'm gonna impress my classmates and math teacher being the class square root human calculator😅😅😅
@mrhtutoring
11 ай бұрын
Great 👍
@_tim
Жыл бұрын
My 2 second approximation would have been “10.something low” and I would stand by it because it’s only an approximation. 😂
@Ennar
Жыл бұрын
You might as well say it's 0 because it's only approximation. The point is that without saying what's the upper bound on error of your estimate, it's meaningless.
@callanc3925
Жыл бұрын
@@Ennar But its not completely meaningless because there are no applications of estimating a square root where an upper bound on the error actually matters. Estimating a square root is for casual conversation and super quick rough working. For any application where you need some level of confidence in the answer you can just use a calculator.
@Ennar
Жыл бұрын
@@callanc3925 I'm sorry, but every single thing you wrote is *completely wrong*. What OP wrote is that they are confident that the correct answer is somewhere between 10 and 11 which is estimating bound on the error. What I wanted to point out that they seem to completely ignore the importance of this by saying "it's only an approximation".
@woegarden
Жыл бұрын
you can tell by the way the chalk glides with ease across the board that this man has put many many sticks of chalk through the ringer. we're talking *holding with your nails* levels of point precision. very talented.
@ocayaro
Жыл бұрын
Hogoromo chalk, that’s the special Japanese invention that’s much coveted around the world.
@Graham_Wideman
Жыл бұрын
wringer
@blackmagick77
Жыл бұрын
I've never been as interested in math as I have been the past 2 days watching random math shorts
@janebrown7231
7 ай бұрын
Brilliant! I love approximation methods. Where I live, young children are taught to approximate before they calculate. It's such a healthy approach.
@majipon7747
Жыл бұрын
here is why this is a good approximation: imagine the closest whole square root as X and the remainder as Y. we are interested in finding: √(X²+Y) he is suggesting this approximation: X + Y/2X let's see what this approximation will give us if we raise it to the power 2: (X + Y/2X)² = X² + Y + Y²/4X² the only difference between this expansion and what we were taking the square root of is the third term (Y²/4X²). and if X is larger than Y this value will be very small. that is why this approximation is good for X>>Y
@KingdomDumb
Жыл бұрын
Finally a good short on my feed. Thank you sir.
@smilekun2825
7 ай бұрын
Nah, this method doesn't work
@willam5065
3 ай бұрын
This is awesome. The skill for quickly estimating is very important in meetings, and for double checking your work and assumptions
@Culebrunch
2 күн бұрын
I was just now 5 min ago having an existential crisis because I apparently completely forgot how to do the long multiplication method on paper until I realized not only was I doing it backwards, I was also applying long addition method rules to it (also doing that backwards as well ffs) so I felt stupid. Thank God I could actually understand and follow through easily with this example. I'm not completely hopeless after all 😂
@jdiv69
Жыл бұрын
I always said its about the teacher. You just taught me something in 60secs that I could never learn in High School. Cheers.
@JimAllen-Persona
3 ай бұрын
I have a similar story. To make it short: I didn’t really understand the fundamentals of Calculus until my daughter’s AP math teacher taught limits some 30 years after I learned it in college. He took 2 weeks to explain limits where my professor made us memorize (and recite on a test) the formal Epsilon/Delta definition of a limit and then moved on. It is about the teacher.
@ronalddg9369
Жыл бұрын
Jeez, it's been so long since I've heard writing on a chalkboard, that really takes me back to elementary school.
@Strawstarberry
Жыл бұрын
The act of writing does more than waste paper and materials. Writing reinforces learning by pairing abstract concepts and thoughts with physical motions that are unique to each written sentence.
@arrheniusleibniz
9 ай бұрын
Newton-Raptson iteration method left the chat.
@nmatthew7469
Жыл бұрын
Good instructor
@Fght..1-.
Жыл бұрын
One of the flaws of this method is that the approximation is only accurate near a square number. If you add a +1 in the denominator of the first derivative term, you get a much better approximation across the entire domain. This corresponds to the piecewise linear approximation of sqrt(x)
@ocayaro
Жыл бұрын
“approximation cannot be accurate” but “close”
@clarenceratkowiak7287
Жыл бұрын
No I myself don't do it either way.
@patricka.crawley6572
Жыл бұрын
@@ocayaroHe is accurate in his approximation.
@Paul-ou1rx
Жыл бұрын
"Google, what is the square root of 102?" Also works.
@tanishianand
10 ай бұрын
Not on a test
@EzaleaGraves
7 ай бұрын
@@tanishianandit 100% works on a test, just gotta be quiet
@gheffz
24 күн бұрын
It is pretty close. Thanks for the tip! Subscribed. All.
@Osprixx
Жыл бұрын
I wish my teachers were like “ya that’s pretty darn close, good job”
@macfrankist
Жыл бұрын
This is actually pretty terrible. Try other values above 102.
@thanosnoctem4473
Жыл бұрын
@@macfrankist No lmao
@macfrankist
Жыл бұрын
@@thanosnoctem4473 Yeah try with 114.
@macfrankist
Жыл бұрын
Sorry I stand ridiculed.
@tmarbut
Жыл бұрын
You can also use the next larger square if it's more convenient. E.g., if we want the square root of 97, we can still start from 10, and then add -3/(2×10) and get a similar approximation. In fact, if the square of an integer you picked is closer to the target number (as 100 is to 97, compared to 81), the approximation will be more accurate.
@xinth23
Ай бұрын
When math is "pretty darn close," I'm all on board.
@XLumens
4 күн бұрын
good teacher.. calm ,to the point..
@derivalz5062
Жыл бұрын
We do it differently. For example, to find sq.root of 56. We take the integers whose square is immediate less and immediate more i.e. 49 = 7², and 64 = 8². So our required number is 7 + (56-49) / (64 - 49). Which is quite close
@momusmomus
Жыл бұрын
Average of taylor expansion from both sides eh
@maxhenderson1890
Жыл бұрын
If you're approximating, you should really be using the ≈ symbol instead of the = symbol.
@mediatour8898
Жыл бұрын
That's awesome bro.
@artemirrlazaris7406
Жыл бұрын
There are various algorithms that can be used to approximate square roots, and different calculators or computing systems may employ different algorithms. One commonly used algorithm is the Newton's method, also known as the Newton-Raphson method. It is an iterative method that starts with an initial guess and refines it through successive iterations to converge to a more accurate approximation of the square root. In simplified terms, Newton's method for finding the square root involves repeatedly improving an estimate by averaging it with the original value divided by the current estimate. This process continues until the desired level of accuracy is achieved. It's worth noting that modern calculators and computing systems often have built-in hardware or software implementations of these algorithms, allowing for fast and efficient square root calculations. ~~Calculating a square root involves finding the number that, when multiplied by itself, gives the original number. Calculators use mathematical algorithms and algorithms to estimate or calculate square roots. There are several methods to calculate square roots, including the Babylonian method, Newton's method, or the digit-by-digit method. These methods involve iteratively refining an initial estimate until a desired level of accuracy is achieved. Modern calculators and computers use algorithms that efficiently approximate square roots, allowing for quick and accurate calculations
@whitekryptonite
Жыл бұрын
Wow, something on youtube where I can learn something. Incredible.
@Aman_iitbh
Жыл бұрын
its can be proofed by eror of √x by taking derivative
@agona4373
Жыл бұрын
I knew this when I was in high school and I had completely forgotten it. Thank you sir!
@robinl3898
10 ай бұрын
Thanks for explaining how to do this. You make it so simple.
@Cobragaming462
Жыл бұрын
Thanks sir... Today, I found a new trick that's applicable for almost every root I hv tried different values and the answers are exactly same, differ in 0.1 or less.. Thanks.. 🙏❤❤❤
@clplusp8762
Жыл бұрын
Or, if you can remember three holidays, then you can easily remember three approximate square roots. Valentines, St Patricks, and Halloween. SR of 2=1.4, SR 3 = 1.7, and 10=3.1
@scoobyflash9768
Жыл бұрын
Also a good way to remember Valentines day
@JimAllen-Persona
3 ай бұрын
Cute trick.
@llspragulus
6 ай бұрын
Love this!!
@vishwajitkumar169
Жыл бұрын
Great video 👍 sir
@ABCDEF-gj8xl
Жыл бұрын
he is like my asian uncle who ask about my math marks
@MediocreDeficit
Жыл бұрын
That's called approximation, done through differential calculus, when i calculate imperfect roots, my friends think im Einstein or sumthin
@blayzcool7897
Жыл бұрын
bro fork everything eles i love how smoothly you write mate
@lesy8068
Жыл бұрын
The old chalk board is more fun than the estimated answer.
@georgeh5075
Жыл бұрын
I have literally never needed to know the square root of a number irl. Thanks school.
@tomaszwota1465
Жыл бұрын
I did. Thanks, school!
@adnansaad3647
Жыл бұрын
Nice, that’s the linear approximation method . Take the nearest number (100 in that case) and write the equation of the tangent line to the graph of sqrt of at x= 100 . The equation will be as follows: y= (x-100)/20 +10 Finally substitute 102 and you’ll get 10.1 Also you can use this method to approximate the values of unpopular angles of trigonometric functions .
I'm still trying to draw the square root sign, then we can get to the numbers. 😂
@andrewmckeown6721
Жыл бұрын
Love how smart people can break things down to simplify things like this. Great explanation.
@gegiojonjongegio7998
Жыл бұрын
The first sqrt(102)=sqrt(100) is triggering me so hard
@Megadumbyog
Жыл бұрын
Waaaaaah waaaaaah waaaaaaaah
@KebabTM
Жыл бұрын
@@Megadumbyog I only see you crying
@Megadumbyog
Жыл бұрын
@@KebabTM I ate your family
@nativeson1559
Жыл бұрын
Wow. Thank you teacher. I’m humbled.
@mayankgidi5790
10 ай бұрын
Is it just me that the noise that the chalk made is extremely satisfying 🤤🤓
@Agent-cv6kh
Жыл бұрын
Use newton raphson method for x^2-n and n^(1/2) is your number
@pelledanasten1615
5 ай бұрын
If the goal is to approximate the square root, saying "approximate the number and take the square root" is not useful. Also this is essentially what he is doing.
@jimmy-j6465
Жыл бұрын
There is a much more intuitive way to work this out, although it is slightly harder. It is known as the concept of small change (an application of differentiation). Only read on if you know how differentiation works :) . Basically, say we want to estimate the value of 3 root 1004 . To do that, let x = 1004, so we have an equation for y = x^(1/3). Differentiating that, we get (1/3)(x^(-2/3)). Using the increments formula, that the change in y = the derivative multiplied by the change in x, we can find the value of root 1000, which is 10. Note that the change in x is 4 (from 1000 to 1004). Then, by substituting x for 1000 and the change in x for 4 in the increments formula, we can estimate the value to be 10+1/75. Please reply if this doesn’t make sense and I will try to explain it to you :) .
@SujalShan-ot8gc
Жыл бұрын
i get the differentiation but dont get the increment formula part \\
@jimmy-j6465
Жыл бұрын
Sure I'll show you :). Basically, the increments formula is that the change in y divided by the change in x equals dy/dx. Multiplying by the change in x, we now get that the change in y equals dy/dx multiplied by the change in x. By subbing in dy/dx= (1/3)(x^(-2/3)) and multiplying both sides by the change in x, we get the change in y equals (1/3)(x^(-2/3)) multiplied by the change in x. Subbing in the change in x=4 and x=1000, we get an estimated value of 10+1/75.
@SujalShan-ot8gc
Жыл бұрын
@@jimmy-j6465 thankyou for taking the time out and explaining. I got it. 🍁
@jimmy-j6465
Жыл бұрын
@@SujalShan-ot8gc You welcome. I'm glad this was helpful :) .
@mattshuey1
7 ай бұрын
Very clean run down and even links it back to it being a quick approximation. Lesser instructors wouldn't have included what the calculator would output, they'd just say here that trick can solve these really quick when it is just a handy trick for approximation. I'm genuinely impressed, so many shorts are clickbaity, this is real education. Guy is very aesthetic looking as well.
@mrhtutoring
7 ай бұрын
Thank you. 😊
@buckwheat6722
Жыл бұрын
Excellent, Thank You!
@diogomiguel2409
Жыл бұрын
Damn it, now i kinda miss math classes
@dylanslingsby
Жыл бұрын
I'd just say roughly 10 and be done with it
@mrhtutoring
Жыл бұрын
Sounds good to me too
@innitbruv2
8 ай бұрын
I’m an engineer and even 10 would have been pretty darn close 😂
@mikefolkestad277
Жыл бұрын
I love these videos when I look at them long enough they make me fall asleep
@cyanidegrapes
Жыл бұрын
Nah yo why did I understand this process in less time than I ever could in high school
@jeffstike3195
Жыл бұрын
Why does math make more sense in a KZitem video then 4 years in school
@NavigatEric
Жыл бұрын
this comment deserves millions of likes. If ANY if my math instructors/teachers had shown us this trick in such a simple way, say anytime between kindergarten to 7 years of grad school for physics ... ? And I finally see it in a youtube video? I might have liked math instead of endured it.
@jamiewalker329
Жыл бұрын
@@NavigatEric Surely you have binomially expanded? (1 + x)^0.5 is approx 1 + 0.5*x, that's school level.
@inspectorgadget346
8 ай бұрын
You pay attention to KZitem. In class your checking out the babes and your mind is elsewhere
@lovesafrica111
6 ай бұрын
Thanks so much....With our school systems failing miserably thanks to gov't intervention, maybe there's hope with teachers like you!! Terrific.
@mrhtutoring
6 ай бұрын
Thank you~
@drewmcmahon2629
Жыл бұрын
I've literally never needed the Sq root of anything even once in my life.
@Votic98
Жыл бұрын
Cause ur cleaining toilets
@FDroid01
Жыл бұрын
Whaaat how not?!
@looming_
Жыл бұрын
what do you do for a living?
@drewmcmahon2629
Жыл бұрын
@@looming_ I work for an ad tech company. What are people (besides math teachers) using it for? I don't even know anyone who has ever used it in real life.
@VegetaIsBetterThanGoku
Жыл бұрын
@@drewmcmahon2629 I use it vaguely as a GC. And I mean very sparingly but I do use it. Say I have a wall that’s 65’ long and need to put decorative trim up and want to do even spaces…. Yea you can split the difference then split it again then again as most contractors would but it’s easier for me to go ok I need 8 boards at approximately 8’ apart plus an additional one as my start piece…. Again the situation rarely comes up but I would be lying if I said I never used it. Curious if anyone else does? 🤔 I also use the Pythagorean Theorem ALL the time. I thought it was useless learning that in school but as a GC I use it constantly. 😅
@ethandeutsch1226
Жыл бұрын
in engineering we draw a squiggle and call it 10
@mjames3662
Жыл бұрын
that's because you don't really need to worry about being precise with engineering and design... things like bridges, tunnels and skyscrapers are typically just eyeballed due to the size 🌉🌁🙌🏽👀. They don't make tape measures long enough... 📏 👷🏽♂️
@zazzletoysbenborkovitz5202
3 ай бұрын
I think this works better if you use the closest square and either subtract or add depending on whether the closest square is higher or lower
@dominicnyabuto6703
Жыл бұрын
I love this approach.
@bc2647
Жыл бұрын
That was awesome
@somedude1666
Жыл бұрын
It's the first 2 terms of the binomial expansion.
@Daniel31216
Жыл бұрын
Not the binomial theorem, but the taylor expansion.
@somedude1666
Жыл бұрын
@@Daniel31216it's the first 2 terms of both. Seriously I got bored one day and checked for it myself on my whiteboard lol.
@Daniel31216
Жыл бұрын
@@somedude1666 Great to know! Now I have the urge to check it out myself.
@richs4878
3 ай бұрын
In the beginning, I figured it’s around 10 and figured I was pretty darn close.
@411sponge72
4 ай бұрын
Ahh gotta love differentials
@alanhurdle3949
Жыл бұрын
Ty I like that
@mrhtutoring
Жыл бұрын
Thanks
@random19911004
Жыл бұрын
This is just expanding the function in a first order (linear) taylor series around the closest perfect square. f(x+h) = f(x) + h* f '(x) f(x) = sqrt(x) and the derivative is f'(x) =1/(2sqrt(x))
@ThoseInterestingStories
2 ай бұрын
What I think is epic about this is that this is using a simplified version of newtons square root function and if you put this value back into the function you can get an even more accurate value
@rabidmyhouse2009
Жыл бұрын
No way I got this right after my big test.
@razataggarwal7365
Жыл бұрын
Derivatives gives you approx results. He should tell the derivatives instead of this magic.😂
@Daniel31216
Жыл бұрын
He is using derivatives, in the form of the taylor series. He's just using the first two terms of it.
@victorlks
Жыл бұрын
√3 ~ .....1.333 is not close to 1.73 so I think it works best for large numbers
@manansharma9164
8 ай бұрын
No. It works best for numbers close to perfect squares.
@ayushmandubey1293
7 ай бұрын
Same with any other random number like √153 if you solve √153 by his method you get 12.084 but the right answer is 12.37
@mrhtutoring
7 ай бұрын
Actually, if you use the method in the video you get 12.375 12+9/(2×12)=12.375
Пікірлер: 3,1 М.