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!

@innovate888

2 ай бұрын

Thanks for your insights.. It's so obvious but hidden at the same time. Thanks again...

@sunburnsam

2 ай бұрын

W.o.W

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_Stowers

3 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.

that's why we use the dot * for multiplication and not the x

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!

@zvonimirkujundzic6867

2 ай бұрын

Beautiful!❤

@zvonimirkujundzic6867

2 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!

@starpier

2 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.

@innovate888

2 ай бұрын

Very interesting observation... :)

@tomctutor

2 ай бұрын

Wisdom gained after the event no doubt.

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.

@mattoucas869

Ай бұрын

True

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

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

Extraordinary result, greetings

Interesting solve. A few steps could be abbreviated and better to avoid using x to denote multiplication when also using it as a variable.

@jaimeduncan6167

2 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.

@mrbenwong86

2 ай бұрын

Should always write x as 𝓧

@DavidDSimon

2 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.

@ukdavepianoman

2 ай бұрын

The early steps are ok, but after around 5:33 it becomes rather ponderous in simplifying the algebra.

@ZigaZagu

2 ай бұрын

Can use * or force parentheses

Очень нравятся Ваши ролики, развлекают лучше фантастики. На скорости 1,5 просто супер! 😍🙋‍♀️

Very cool problem and solution!

@learncommunolizer

Ай бұрын

Thank you very much!!

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😂

@innovate888

2 ай бұрын

Thank You for your insights.. God Bless YOU and your Ancestors too :)

@amankumar-set

2 ай бұрын

Your ancestors must be followers of Aryabhatta.❤

@lylechen8881

2 ай бұрын

😂😂😂 哈哈！牛逼

@Xingzi786

2 ай бұрын

😂😂

@dukeofglasgow9354

2 ай бұрын

In the test you have to show the long solution to get high score so you can’t just use approximation 😂

Beautifully done!

Clever. 😊

Pretty fancy way to write three!

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.

I never really watched yt that much until I found your channel

Nice math quest!

The denominator is obviously 11111111^2, the rest easily follows as this type of Q usually has rational answer

Amazing

@learncommunolizer

Ай бұрын

Thank you very much!!

Dear Friend: Excellent Video !!! Your work was incredible..!!! I enjoyed the journey and numerical gymnastics you presented :)

I like how you say hello.

That was crazy. All that to get 3. Niiiiiice

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.

Perfect 🎉🎉

@kiransankarkar6966

2 ай бұрын

Very good (India)

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.

😮😮😮 Wonderful maths is so beautiful

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

Exvellent work my friend

@learncommunolizer

Ай бұрын

Thank you very much!!

great!!!!

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

nice

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

@danilomendesdasilva2586

2 ай бұрын

As an Engineer myself I Agree with your simple solution.

@seilaoquemvc2

2 ай бұрын

This is far and away the best solution here

@williammendieta5427

2 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.

@tripplefives1402

2 ай бұрын

I watched the video at fast speed and got the answer in 28 seconds. Try harder next time.

@owhale

2 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.

Oh my.... wonderful math

@learncommunolizer

Ай бұрын

Thank you very much!!

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.

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.

The result is absolute value of 3

@ZAWARUD00

2 ай бұрын

Absolute value of 3 is 3 FYI

@hiryu70

2 ай бұрын

​@@ZAWARUD00 how about -3? It is not 3, but will be correct in case of absolute value of 3

@MenelBOT

Ай бұрын

​@@hiryu70 the absolute value of -3 equals the absolute value of 3, but they are not the same.

The Doctor of Arithmetics!!! Ar.D.

Wow😊

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

Brilliant.

@learncommunolizer

Ай бұрын

Thank you very much!

Add numerator(n) + denominator(d), you get 10 times denominator => n+d=10d n=9d n/d =9 (n/d)^0.5 =3

Nice

@learncommunolizer

Ай бұрын

Thank you very much!!

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.

beautiful :)

The top one is the multiplication pattern 3 × 3, 33 × 33... and the botton one is 1 × 1, 11 × 11... The answer is three.

Wow unbelievable😂

Great. Thanks!

@learncommunolizer

Ай бұрын

Thank you very much!!

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.

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.

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

What kind of math knowledge is needed to solve this. You're either lucky or you're not. Ridiculous.

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

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.

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

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

Красивая задачка)))

@rocket247

2 ай бұрын

придуманная с конца

very easy

Вы волшебник!

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).

No thanks, i'm good. Have a nice day. Goodbye.

it is 3 or -3. Great approach anyway. Regards.

@nikolayparygin610

2 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

@justaboutanything9378

2 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

@victoriamacarthur8906

Ай бұрын

it is just 3 tho

Everytime she say "over" its always remind me of wall-e saying "eve", love ur vid

Hellom is wonderful

おもしろい！

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.

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

Jojo gracias !!

Surprisingly the answer was a simple 3 That just made my day 😂

I participante at the Brazilian math olypmics of public Schools

👍

В следующущий раз попробую поделить в столбик😊 Пример специально подобран так, чтоб не всякий калькулятор осилил)

Pretty cool

@learncommunolizer

Ай бұрын

Thank you very much!!

By count ing the digits, 16 digits / 15 digits number, assuming the answer is integer, i guess it is sqrt(9) = 3

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 . . .

@nefer3195

2 ай бұрын

Yeah... Try writing "The answer is clearly 3" in a math copy, see if the corrector likes that.

This is so useful, like when... Wait. 🤔

❤❤❤❤❤❤❤❤❤

The top is divisible by 9, which is clear because all the digits add up to a number divisible by 9. Once the 9 is factored out, the numerator is just 123456787654321, which cancels out the denominator. So sqrt(9) = 3.

divide numerator by 9 manually, and you will see the magic

Wait, in the middle of √, is that ok to have + or -?

@GranttheSATGenie-tc9oi

2 ай бұрын

Yes this is fine, so long as we observe the order of operations and evaluate these prior to taking the root.

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

Nice. Anyway it is stupid to use the same symbol (x) for multiplication and as a number.

🤯🤯🤯

This kind of Math Olympiad Questions singles out kids who spend too much time inside, not the bright ones.

Sqrt(9)=+-3

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.

@nikolayparygin610

2 ай бұрын

корень из 9 не может быть отрицательным?

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.blockcraft6633

2 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

Took be about 10 seconds to divide mentally both num. and den. by 11111111

And ooooovvvvvaaaaaa😅

I can't believe after doing all this he missed the ±3

It's cute, but real life, how often do such obvious practical transformations actually come up? (Not math competitions, but everyday life, include science nerd topic viewing?) For large numbers, this is FAR FAR less likely than doing a trick like converting a number near, say, 100 to 100, to make a calculation like multiplying easier. Maybe I'm just getting old. I enjoy number theory, recreational math, etc, but I enjoy it for relatively general applications, not something that's a "trick" which I'll almost never see again aside from (perhaps) some highly specialized math puzzle solving domain. At least I did recognize the major patterns re both the numerator and denominator, leading to using 11111111 right away, though I didn't realize how helpful using X in place of that would be, re the whole problem. (Math was always my worst STEM subject, compared to the SERIOUS math people). And I'm way too rusty (it's been 45ish years since college math classes) that I would have worked out the answer in any reasonable time frame, even having made the 11111111 identifications. So kudos for a very clever, clear presentation.

3

Mən 5 saniyədə tapdım cavabı. Yuxarıdakının sonu 9, aşağıdakının sonu 1 edir. Məntiqlə 9-a bölünüb. Kök altı 9 da edir 3.

На калькуляторе вы сможете посчитать это за 10 секунд. Без калькулятора вам понадобится истратить много бумаги и много времени. Вывод: покупайте калькулятор!

Это великолепно, но у меня есть калькулятор.

А ещё :a=-7, b=0

The only thing I have learnt here is 111.. X 111.. = 1234..4321.

It's an interesting puzzle, but it looks like jumping on your balls if you don't use CAS or calculator to solve something like this in real life. If I would be interested in fine and accurate solutions, the first thing I might do is the factorization both of the devidend and the divisor.

Joli petit exemple de calcul 👍. C'est aussi un bon exemple d'étude de rédaction. Comment faire pour rédiger d'une manière plus courte et beaucoup moins fastidieuse ? On va utiliser un petit peu D'ABSTRACTION et quelques LETTRES et prendre un peu de RECUL : Pour bien comparer les deux rédactions, comme lui, je ne vais pas écrire les commentaires. Ma rédaction commence donc ici. On va éviter de recopier la racine et on va couper en morceaux. quotient sous la racine = N/D Calculons D seul X=11111111 (8 fois le 1) 111x111 = 12321 etc. donc D = X.X = X^2. (👍) Calculons N seul: N = 1111111000000000 + 88888888 + 1. (au début 7 fois le 1 et 9 fois le 0) N = 11111110.10^8 + 8.11111111 + 1 et on introduit X Or 11111110 = X - 1 N = (X - 1).10^8 + 8X + 1 on développe N = 10^8.X - 10^8 + 8X + 1 = 10^8.X + 8X - 10^8 + 1 or - 10^8 + 1 = - 99999999 = - 9X N = 10^8.X + 8X - 9X = 10^8.X - X N = X(10^8 - 1) = X.9X (voir ligne d'avant) = 9X^2 (cool) donc N/D = 9X^2 / X^2 = 9 donc le résultat est rac(9) = 3. Beaucoup plus court, plus clair, plus rapide, donc moins de fautes et beaucoup plus facile à refaire. 😉. Même en maths la rédaction ça compte. L'ABSTRACTION est indispensable et ça aussi ça S'APPREND . Encore merci pour ton joli calcul.

+ - 3