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Пікірлер: 264
@digitalcurrents2 ай бұрын
If you're notating x to mean multiply, don't use x as a variable. Or if you're keeping x as a variable, use the * to notate multiplication.
@Steve_Stowers29 күн бұрын
Yes, I would have picked a different letter, both for that reason and because x typically represents an unknown variable, not a known constant. Other than that, though, this is a good solution.
@Serisky62124 күн бұрын
I agree 1000%. Using x to mean multiply and to stand for a number at the same time can be very confusing or ambiguous. For example, 5xt can mean either "5 times t" or "5 times x times t" That's why x is generally not used in algebra to mean multiply. I also agree that x, y, z, t and other letters typically used for unknown or changing values should not be used for constants to avoid confusion.
@johnblake66153 ай бұрын
I used a trick: usually the result is very simple. So if it's a square root, than probably the number under the square root could be sth like 4,9,16... Let's do a quick test and get the approximate value of the division: the numerator has 16 digits and the denominator has 15..so it will be close to 11/1,2 and it is something a bit less than 10. Could it be 9? Let's check the nominator if it is divisible over 9. It is. Let's try to multiply the divisor by 9. It worked!
@innovate8883 ай бұрын
Thanks for your insights.. It's so obvious but hidden at the same time. Thanks again...
@sunburnsam2 ай бұрын
W.o.W
@holz_name2 ай бұрын
that's why we use the dot * for multiplication and not the x
@dsamuelis2 ай бұрын
Why so complicated? 16 digits over 15 digits, and after the addition / subtraction the last digits of numerator and denominator are 9 and 1, respectively. So the last (and only) digit of the quotient must be 9. To test just multiply the denominator by 9 and it checks. Sqrt(9)=3. Done.
@mattoucas8692 ай бұрын
True
@is77283 ай бұрын
Actually the numerator 1, 111, 111, 088, 888, 889 = 33, 333, 333^2. And as for the denominator 123, 456, 787, 654, 321 = 11, 111, 111^2. So after being sqaure-rooted, the number becomes 33, 333, 333 / 11, 111, 111 = 3. And this is the answer!
@zvonimirkujundzic68673 ай бұрын
Beautiful!❤
@zvonimirkujundzic68673 ай бұрын
You are wright, but without calc you couldnot know a value of numerator and denominator! Our beautifull lady was show the nice trick how to do this! Thanks her!
@starpier3 ай бұрын
@@zvonimirkujundzic6867 also the trick shown in the video requires that you identify the denominator as a number at the power of 2. Without a calculator is not simple to guess in any case.
@innovate8883 ай бұрын
Very interesting observation... :)
@tomctutor3 ай бұрын
Wisdom gained after the event no doubt.
@ukdavepianoman3 ай бұрын
Interesting solve. A few steps could be abbreviated and better to avoid using x to denote multiplication when also using it as a variable.
@jaimeduncan61672 ай бұрын
Some people can't follow if he starts to skip steps, the ones with more practice can be like "Factor the nine already" but we lost nothing. On the other hand, someone with less practice could get lost. I guess the channel is for everybody is not like this is a problem on Lie Algebras or the version of functional analysis that we use in physics.
@mrbenwong862 ай бұрын
Should always write x as 𝓧
@DavidDSimon2 ай бұрын
Yeah - no need for all those steps. Just look at the numbers - answer top division is clearly just a little under 10. And with a denominator ending in 1 and numerator ending in 9, 9 is the obvious answer to the division problem. Far more math work than needed to actually solve.
@ukdavepianoman2 ай бұрын
The early steps are ok, but after around 5:33 it becomes rather ponderous in simplifying the algebra.
@ZigaZagu2 ай бұрын
Can use * or force parentheses
@solution1203 ай бұрын
In China, we use the following method to do this kind of questions( We never tell anybody this secret. Today I have to make a decision that goes against my ancestors😇) . 11/1.2=9.16 so answer is 3😂
@innovate8883 ай бұрын
Thank You for your insights.. God Bless YOU and your Ancestors too :)
@amankumar-set2 ай бұрын
Your ancestors must be followers of Aryabhatta.❤
@lylechen88812 ай бұрын
😂😂😂 哈哈!牛逼
@Xingzi7862 ай бұрын
😂😂
@dukeofglasgow93542 ай бұрын
In the test you have to show the long solution to get high score so you can’t just use approximation 😂
@PedroOrtiz-sh8hs3 ай бұрын
Extraordinary result, greetings
@lornacy3 ай бұрын
Pretty fancy way to write three!
@vabka-77082 ай бұрын
Brutforced this one. 1. sqrt(a)/sqrt(b) = sqrt(a/b) 2. Answer should be simple so a/b should be integer and complete square 3. 1111111088888889 can be divided by 9 because 7*1+7*8+9 = 8*9 4. Take a minute to carefully divide it. 1111111088888889 / 9 = 9 * 123456787654321 5. sqrt(9*123456787654321 / 123456787654321) is trivial. Answer is 3 But your solution is more elegant
@trackinggod80872 ай бұрын
Very cool problem and solution!
@learncommunolizer2 ай бұрын
Thank you very much!!
@adjadiop44102 ай бұрын
😮😮😮 Wonderful maths is so beautiful
@NoahM.Angell-sd4ez3 ай бұрын
I never really watched yt that much until I found your channel
@Frostnburn4 күн бұрын
The way I did it was, check the last digits of the nominator and the denominator (9 and 1 respectively) and determine what the trailing digit of the quotient is, in our case it's 9 (the last digit of a product is determined only by the last digits of the numbers being multiplied together), but given that the top line has 16 digits, the bottom only has 15, and the left most two digits of the top is smaller than the left most two digits of the bottom, there is a good chance that the quotient is 9. To confirm that, either do a long division, or multiply the bottom by 9 to see if we get the top, or add the top and bottom together and see if the sum is exactly 10x the bottom, I chose the latter since adding is much faster than multiplying. The result was that the sum was indeed 10x the nominator, so the whole fraction reduces to 9, leaving it's square root as 3
@theresaotoole91413 ай бұрын
I did it less than 30 seconds (in my head) and got 3: 16 digits on top 15 on bottom - 1111/ 123 = about 9 and sq of 9 = 3
@danilomendesdasilva25863 ай бұрын
As an Engineer myself I Agree with your simple solution.
@seilaoquemvc23 ай бұрын
This is far and away the best solution here
@williammendieta54272 ай бұрын
Although I agree this is the fastest and the most parsimonious way, this is an aproximate Solution. Plus, there is a certain beauty in seeing how the numbers are transformed along the way. Fast is good, But is not always better.
@tripplefives14022 ай бұрын
I watched the video at fast speed and got the answer in 28 seconds. Try harder next time.
@owhale2 ай бұрын
Well done only if you are an engineer. But if you are an engineer you are an idiot not to use a calculator.
@stigmontgomery79013 ай бұрын
Beautifully done!
@kevinbyrne45383 ай бұрын
Clever. 😊
@innovate8883 ай бұрын
Dear Friend: Excellent Video !!! Your work was incredible..!!! I enjoyed the journey and numerical gymnastics you presented :)
@Vladimir_Java_dev2 ай бұрын
Nice math quest!
@zanicar408728 күн бұрын
Took me a couple of seconds to determine it is 3... but only because I was looking at repeating number square patterns during the past week. I recognized the top to be the pattern for 3 (1..08..9 the number of 1s or 8 indicates the number of repeating 3s); and the bottom to be the pattern for 1 (123..321 with the highest number at the inflection point indicating the number of repeating 1s)... 3333 3333 / 1111 1111 = 3
@Ron_DeForest2 ай бұрын
That was crazy. All that to get 3. Niiiiiice
@mata272317 күн бұрын
Very nice solution !
@user-eu1fr7hk4yАй бұрын
Очень нравятся Ваши ролики, развлекают лучше фантастики. На скорости 1,5 просто супер! 😍🙋♀️
@chadgillis54792 ай бұрын
Exvellent work my friend
@learncommunolizer2 ай бұрын
Thank you very much!!
@pitdog753 ай бұрын
I like how you say hello.
@knotwilg35962 ай бұрын
Set x =11111111 Observe that the denominator is x² adding x to the numerator gives 1111111100000000 = 10^8 * x = (9x + 1) * x = 9*x² + x , so the numerator = 9x² so the fraction is 9 and the square root of that is 3. The key elements are "seeing" step 2 and 3 of which 2 is the hardest. As others have pointed out, the alternative way is suspecting that the fraction equals 9, by estimation, then checking it is.
@ufukkoyuncu340812 күн бұрын
perfect question
@karantindead2 ай бұрын
great!!!!
@alexatg1820Ай бұрын
The denominator is obviously 11111111^2, the rest easily follows as this type of Q usually has rational answer
@vedatataman5598Ай бұрын
Wow😊
@alexeystrizhevski2398Сағат бұрын
The sum of the digits in the numerator is 1*7+0+8*8+1=72. 72 is divisible by 9 without a remainder. Divide the numerator by 9 and get a number equal to the number in the denominator. As a result, we get the square root of 9*1, and we get 3. Magic? No - mathematics.
@gunfoogunfoo22872 ай бұрын
The Doctor of Arithmetics!!! Ar.D.
@dougaltolan30172 ай бұрын
Could have gone straight to long division, writing out the 123456787654321 times table by repeated addition. As soon as you hit 123456787654321 x 9, the answer pops right out. Might even be quicker too, but it assumes that the answer is going to be simple.
@daniilvolfengaut883828 күн бұрын
beautiful :)
@UnfunnyGaming992 ай бұрын
Got it in 10 seconds. I already knew the property of repeating 1s and 3s when squaring, so that led me to get 3 as an answer
@chigozie1232 ай бұрын
Amazing
@learncommunolizer2 ай бұрын
Thank you very much!!
@prince891023 ай бұрын
Perfect 🎉🎉
@kiransankarkar69663 ай бұрын
Very good (India)
@RickB5002 ай бұрын
Great. Thanks!
@learncommunolizer2 ай бұрын
Thank you very much!!
@theeraphatsunthornwit62663 ай бұрын
Wow unbelievable😂
@zsoltdr.ajtony80943 ай бұрын
nice
@sparkyshore3543Ай бұрын
All you have to do is recognize the numerator is divisible by nine, do the long division (which isn’t hard), and realize that the quotient is also the denominator. Cancel and take the root and the answer is three.
@finmat952 ай бұрын
No thanks, i'm good. Have a nice day. Goodbye.
@alnitaka2 ай бұрын
I note that the numerator is really 11111111*sqrt(9), from which the result follows. So it won't work in base 12. There you get 11111111*sqrt(e) where e is the digit eleven. The square root of eleven is irrational. It works for bases n^2+1 where n is an integer. For example, sqrt(1111111033333334) in base 5 is 22222222 in base 5.
@diegoveron9962 ай бұрын
Jojo gracias !!
@saarike2 ай бұрын
Oh my.... wonderful math
@learncommunolizer2 ай бұрын
Thank you very much!!
@martingibbs89725 сағат бұрын
How did you find such a slow method?! The method described by many of the comments is much quicker.
@alexis-sk9vf2 ай бұрын
я методом подбора определил, что числитель делится на 3 и вынес 3 за скобки, затем ещё раз сделал то же самое, в скобках осталось число равное знаменателю. Определить делится число на 3 можно посчитав сумму всех его цифр. Если она делится на 3, то и всё число делится на 3. Но это не честный вариант, хотя и без калькулятора, и два раза пришлось делить столбиком.
@nouration968528 күн бұрын
I kinda just lucked out, I felt the numbers were too specific so it was probably a round number, I tried subtracting them got nothing, then I tried adding them (1,111,111,088,888,888 + 123,456,787,654,321) and got 1,234,567,876,543,210, which as you can see gives the bottom number multiplied by 10, so if x + y = 10y, then that means x = 9y, the top number is the bottom number multiplied by 9, so the division gives 9, so the answer is 3, the square root of 9
@vikapm2 ай бұрын
You can also realize that 1111111088888888 = 1111111100000000 - 1 - 11111111 Then 1111111088888888 + 1 = 11111111E+8 - 11111111, or 11111111 x (1E+8 - 1) Dividing by 11111111^2, you get (1E+8 -1) / 11111111, or 99999999/11111111 = 9
@raihanfitriansyah23722 ай бұрын
Everytime she say "over" its always remind me of wall-e saying "eve", love ur vid
@oDTR2 ай бұрын
I participante at the Brazilian math olypmics of public Schools
@spacedust48673 ай бұрын
おもしろい!
@mariats28653 ай бұрын
Вы волшебник!
@GranttheSATGenie-tc9oi2 ай бұрын
I love the solution, very formal and step by step. I did it a different way, and I'm glad i tried before watching your method, as i wouldn't have noticed this trick if not for my stubbornness: I decided to factorize the numerator (having recognized that the denominator is 11111111^2). Applying a quick divisibility check to the numerator reveals 9 as a factor (digit sum is divisible by 9). Once you start long dividing the numerator by 9, you'll see the beautiful number 123456787654321 emerge as the quotient. It's quite pretty. So those giant factors cancel leaving root 9 equals three as the answer.
@iangmk2 ай бұрын
Do the addition and the substraction, then multiply numerator and denominator by 9. The result inside the square root is: (1111111088888889)*9/1111111088888889. Simplify. The result inside the square root is 9. So, the solution is: +-3
@juanpablolayerenza3 ай бұрын
The result is absolute value of 3
@ZAWARUD002 ай бұрын
Absolute value of 3 is 3 FYI
@hiryu702 ай бұрын
@@ZAWARUD00 how about -3? It is not 3, but will be correct in case of absolute value of 3
@MenelBOT2 ай бұрын
@@hiryu70 the absolute value of -3 equals the absolute value of 3, but they are not the same.
@craigkdillon2 ай бұрын
Brilliant.
@learncommunolizer2 ай бұрын
Thank you very much!
@ryan-heath2 ай бұрын
Surprisingly the answer was a simple 3 That just made my day 😂
@oleganisimov90043 ай бұрын
Красивая задачка)))
@rocket2473 ай бұрын
придуманная с конца
@subramanyakarthik5843Ай бұрын
Directly add 1 to get perfect square of numerator which can be written as 1111111 × 9999999 / and denominator as 1111111^2 Which can be divided by 9 therefore getting sqrt value of 9 which is 3
@androlsaibot2 ай бұрын
I found the sqrt of 1111111088888889 in the same way as with the divisor, by starting the sequence with sqrt(1089), which must be a bit larger than 32 = sqrt(1024), so I tried 33, it worked. I noticed that 3 is sqrt(09) where 09 is the first iteration of the number and 1089 the second, so I had the sequence, where for 1111111088888889, which is the 8th iteration, the sqrt must be 33333333. Dividing by 11111111 gives 3.
@falklumo2 ай бұрын
This kind of Math Olympiad Questions singles out kids who spend too much time inside, not the bright ones.
@artemponomar93692 ай бұрын
Проверить разложение числителя на множители, делится на 3. Разделить на 3, проверить разложение, понять что делится еще на 3. Разделить на 3. Сократить числитель и знаменатель.
@escanorsama5823 ай бұрын
very easy
@dmitrmax2 ай бұрын
Sum of digits in nominator is divisible by 9, that is why the nominator is divisible by 9. If you divide it - you will get denominator.
@user-xk8fl7fc5tАй бұрын
👍
@SillyPerrin2 ай бұрын
Pretty cool
@learncommunolizer2 ай бұрын
Thank you very much!!
@user-sv9op5ec9x2 ай бұрын
I did it extremely fast 33^2=1089 , 333^2=110889 11^2=121 ,111^2=12321 , followed by pattern ans will be the sqrt of 3333333^2/1111111^2= 3
@AyushTH2 ай бұрын
The top one is the multiplication pattern 3 × 3, 33 × 33... and the botton one is 1 × 1, 11 × 11... The answer is three.
@davidbergeron782 ай бұрын
Nice
@learncommunolizer2 ай бұрын
Thank you very much!!
@djconnel2 ай бұрын
This is nuts. Although if I'd just taken the first 3 digits I'd have gotten sqrt(111/12) which is around sqrt(9) = 3. So I could have gotten a very good estimate.
@rosamariavercelloni17192 ай бұрын
❤❤❤❤❤❤❤❤❤
@user-jr6ue7rk9p2 ай бұрын
В следующущий раз попробую поделить в столбик😊 Пример специально подобран так, чтоб не всякий калькулятор осилил)
@rafazieba99822 ай бұрын
What kind of math knowledge is needed to solve this. You're either lucky or you're not. Ridiculous.
@HarshRaj-yj5gbАй бұрын
Add numerator(n) + denominator(d), you get 10 times denominator => n+d=10d n=9d n/d =9 (n/d)^0.5 =3
@mohamedforsane241222 күн бұрын
عجيب.....ههههه
@mintplay3295Ай бұрын
111111108888889 (numerator) can be written as 1111111 x 9999999 and denominator can e written as 1111111² and after cancelling out everything we end with √9 = 3
@user-en3yt4lu8l2 ай бұрын
divide numerator by 9 manually, and you will see the magic
@user-ey3ng3kv1h22 күн бұрын
بعد نكملوا 😊😊😊...👍
@abdulayaan6352Ай бұрын
🤯🤯🤯
@axelkidd98503 ай бұрын
This is so useful, like when... Wait. 🤔
@the_visapurkar40442 ай бұрын
And ooooovvvvvaaaaaa😅
@gersimy2 ай бұрын
Много единиц и восьмерок - проверяем делимость на 9. Числитель делится, знаменатель нет. Делим числитель на 9 в столбик - получаем знаменатель. Получаем, что значение выражения - корень из 9, т.е. 3
@yorktsang2 ай бұрын
By count ing the digits, 16 digits / 15 digits number, assuming the answer is integer, i guess it is sqrt(9) = 3
@xgx89926 күн бұрын
Well presented, but in reality this problem only tests whether one knows that 111...^2=... No real reason to learn, remember, or teach this rule (unless you aspire to be a number theorist).
@lorenzonieto7672 ай бұрын
Lo resolví en 5 segundos y no por hábil sino por lo predecible. Me dí cuenta que, multiplicando el denominador por 9 daba como resultado el numerador. Raíz de nueve tres. Fin
@przejan2 ай бұрын
it is 3 or -3. Great approach anyway. Regards.
@nikolayparygin6102 ай бұрын
@@justaboutanything9378 x doesn't matter. (any number)^2 woudl be positive. as soon as we have positive numbers in square root we shoud consider negative outcome
@justaboutanything93782 ай бұрын
@@nikolayparygin610 you are absolutely right, I mixed up the fact that we only solve for positive value of y when in √y situation, I'll delete my previous comment oopsie
@victoriamacarthur89062 ай бұрын
it is just 3 tho
@hasanalma83202 ай бұрын
Sqrt(9)=+-3
@rahuldey5564Ай бұрын
I can't believe after doing all this he missed the ±3
@tontonbeber4555Ай бұрын
Took be about 10 seconds to divide mentally both num. and den. by 11111111
@schurlisuper390928 күн бұрын
Nice. Anyway it is stupid to use the same symbol (x) for multiplication and as a number.
@karzo_manager2 ай бұрын
Я решил так. Я знаю, что числа 11, 111, 1111 во 2ой степени имеют вид: 11^2=121 111^2=12321 1111^2=1234321 И так до 11111111^2=123456787654321 В числителе сумма цифр кратна 3, значит делим в столбик 1111111088888889, получаем 37037032962963, опять сумма цифр кратна 3, опять делим на 3, получаем число 123456787654321. Итак теперь выражение имеет следующий вид: sqrt(11111111^2 × 3 × 3/11111111^2) = sqrt(9) = 3 Потратил всего 1.5 минуты на данное выражение.
@nikolayparygin6102 ай бұрын
корень из 9 не может быть отрицательным?
@DavidDSimon2 ай бұрын
Starting with the assumption that this is only going to be given as a no calculator problem if you're dealing with whole numbers .. . takes 3 seconds to solve. Answer is clearly under 10 but clearly just about 1 under 10. And denominator ends in 1, numerator 9 so that checks. Answer is 3. If you're going to use a "trick" why use a trick that takes that much math . . .
@nefer31952 ай бұрын
Yeah... Try writing "The answer is clearly 3" in a math copy, see if the corrector likes that.
@Anti_During9 күн бұрын
Решил по формуле Пика за 0.0000016 секунды
@gokalp42182 ай бұрын
3
@manudude022 ай бұрын
well, that was a lot more complicated than you had to make it. If you observe number in the square root is (11111111*10^8-11111111)/11111111^2, you can reduce it to 10^8-1/11111111, which is 99999999/11111111, and the square root of 9 is +/- 3
@dr.blockcraft66332 ай бұрын
Sqrt(9) = 3. Not ±3. You always Take the Principle (positive) root. You only Go that Route if Your using The inverse Of a Number Squared. eg x² =9 x =±3
@byt53 ай бұрын
Это великолепно, но у меня есть калькулятор.
@thebasisti24823 ай бұрын
😳
@abdulgh43412 ай бұрын
Lass es so😂
@IamtheMan11113 ай бұрын
Wait, in the middle of √, is that ok to have + or -?
@GranttheSATGenie-tc9oi2 ай бұрын
Yes this is fine, so long as we observe the order of operations and evaluate these prior to taking the root.