China | Math Olympiad | A Nice Algebra Problem 👇

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[@jerryliu1446]

I have a easier way to do this without the boring caculation part. We first definite algebra A as 11111 and swap the big number in square root with algebra A √(4444488889)=√(4A x 10^5)+8A+1=√4Ax(9A+1)+8A+1=√36A^2+12A+1=√(6A+1)^2=6A+1=66667

[@arasu18]

Yes the question 4s 8s and 9 makes us think in (A+B)^2 logic 👍🏽

[@edwinpittomvils2570]

Just use Newton iteration f(x) =x^2-a gives next x = (x^2+a)/2x. Start wit x = 67000 and after one iteration you are spot on 66667. Doesn’t take 3 minutes!

[@6bq7aez80]

Pourquoi commencez vous par 67000? D'où provient cette valeur ou comment la déterminez vous?

[@Devishhike]

@@6bq7aez80 Maybe because the given number has 10 digits so square root has D / 2 digigts. 10^a^b = 10^(a*b). 67^2 and 66^2 is closest to 4444, 4489 and 4356 respectively.

[@6bq7aez80]

​@@Devishhikemerci. Je dois avouer que je ne connais pas par cœur les carrés des nombres bien au delà de 16 et je n'aurais pas pu trouver en moins de 3 minutes.

[@Devishhike]

@@6bq7aez80 It's all about evaluation. For instance, 3600 is 60^2, so u may start Newton method with 60. Ok, even though you know that 4^2 is 16 then u can go on with 5^2 is 25, 6^2 is 36 and 7^2 is 49, so our result begins with 6 because the first 2 digits is 44 and the nearest value which is lower and is a square is 36. There is a manual square root algorithm with pen and paper (which does the same process I've described) u can look for it.

[@6bq7aez80]

@@Devishhike la dernière racine que j'ai arrachée n'était pas carrée et re-apprendre à extraire une carrée m'aurait pris déjà les 3 minutes. 3mn vous sont une éternité mais pour moi un clin d'oeil. Merci d'avoir satisfait ma curiosité .

[@Nr_Logic]

Nice solution

[@arvindkulkarni6580]

Very well explained such complex question

[@leealex3692]

amazingly stupid solution

[@tamirerez2547]

Nice problem and excellent solution.👍 But you have to work on your 8's... 😉

[@erwanallot6298]

Bravo, merci beaucoup.

[@Pomskywalker]

Love the way you taught. It's a good example to solve a big question by using basic algebra. Thank you so much.

[@vengurlajoshi5003]

Good food for thought. Thank you

[@anderlecht1969]

Just fantastic

[@user-go5sy7mu6q]

Mast hey ye video

[@hindjind]

जुगाड करने की कला ही गणित कहलाती है,

[@ronaldnoll3247]

Very, very good... I am impressed

[@user-yt1wp2jn4w]

x=11111,10^5=9x+1: 4444488888+1=4x*10^5+8x+1=4x(9x+1)+8x+1=36x^2+12x+1=(6x+1)^2

[@makotoishizuka6479]

It's easier to just do the square root using written calculations.

[@ahmadhabibi3348]

a reasonable solution but difficult to repeat without seeing this method

[@leealex3692]

AMAZINGLY STUPID SOLUTION, just let X=11111, 10^5=9x+1

[@harshpathak2359]

Nice simplified

[@leealex3692]

amazingly stupid solution

[@manojchaugule794]

its very good simplified

[@nguyenvannhan2127]

Do we need to solve these problems to become rich? My boss stopped studying when he was 10 and now he has 10 Million dollards 😂

[@jameswachira-fu6lk]

that's great😄😄😄

[@olegdmitriev6854]

The mutual strikethrough of the square root and the degree of the number inspired me incredibly. It is possible that this should be done in the rice fields of a Chinese village... In our fifth grade, a schoolboy would be sent for his parents to find out how mentally complete this schoolboy is. But even for a schoolboy of an average rural Chinese school, the square root is actually a two-digit function. However, it is possible that China has a different algebra... I fell into prostration from the level of teaching algebra in China.

[@kathyasmith9999]

Too long for practice life, only for knowlodge. Is very very good

[@LaxmanKumar-yi4cv]

Nice explanation mam

[@harikishan1900]

Very well 😊

[@satyadev3848]

great😊

[@saswataghoshlearning4361]

simple division process can do it in 2 mins why to do so much but process was good

[@arnoldli4051]

Amazing

[@govindbhaipatel8253]

Deep knowledge

[@Chiavaccio]

👍👍👍

[@ivanku.2049]

also -66667 is another solution

[@leealex3692]

wrong ONLY 66667

[@abibfaye3026]

Yes you’re done

[@abibfaye3026]

@@leealex3692it’s not wrong

[@rmorenod83]

Only one solution! You're not solving an equation x² = .....

[@wenardiardi1963]

Result of squareroot is positive. Unless theres an imaginary number

[@Maheshkumar-cw6un]

Perfect learning

[@leealex3692]

AMAZINGLY STUPID SOLUTION, just let X=11111, 10^5=9x+1

[@leohkhung]

very interesting

[@user-mc5pg4do4z]

There mistake in second line

[@johnnyjoe9904]

Lot of time you can find by division method quickly

[@adenwellsmith6908]

Lose a mark for no negative root.

[@葉永福]

直式開方更容易

[@user-vf4lm1lp2n]

嘿，你有學到直式開根號，不錯。

[@kimwonyoung_]

너무 반짝반짝 눈이 부셔 노노노노노 너무 깜짝깜짝 놀란 나는 오오오오오 너무 짜릿짜릿 몸이 떨려 지지지지지 오 젖은 눈빛 오 예 오 좋은 향기 오 예예예

[@samherat7302]

Why not the conventional method that may take shorter time?

[@aruntiwari5714]

❤❤❤❤

[@RealQinnMalloryu4]

(x ➖ 3x+2).

[@RealQinnMalloryu4]

2^2^2^2^2^2^2^2^2^2^2^32^3^2^32^3^3^2 1^1^1^1^1^1^1^1^1^11^1^1^1^1^1^2^13^1 23 (x ➖ 3x+2) .

[@user-bj9sj1mj4z]

one two tree four five 🗣

[@91873delete]

It gave me slap on what I lost doing and thinking when i was a child

[@bambangnugroho6147]

Your process make your head dizzy. You should using CAS to solve it. Mathematic is learning, the scientist making calculator and computer, why you doubt them ? You better at cooking masala.

[@user-mc3bu1lb7g]

Столько лишних действий, глупых и не нужных, похоже чтоб тайминг растянуть, мне бы за такое решение 3 поставили.

[@ThuNguyen---]

Thời đại 4.0 lấy máy tính bấm chưa đến 1 giây ! Làm dài dòng quá !

[@muharrem9006]

And minus of the solution you found also will be another solution. Plus-minus

[@AlbertoDiezfibracity]

Mucho más corto calculando la raíz cuadrada a mano

[@user-em3pn6fk9d]

この発想は無かったー！

[@ruslanbip7333]

did it wo paper in less than 30 secs

[@Stn_4]

Try log

[@paporot06]

У стовпчик - куди скоріше.

[@jefferychow4765]

99999 is not "five times nine"...

[@user-se5wr3sd5y]

Красивое решение!

[@user-vf4lm1lp2n]

做的很努力，但冗長複雜，效率不佳，直式開根號可直接算出。

[@user-wd7gy1um9l]

scam

[@user-uz2fz5px1o]

Τόσος υπολογισμός για το τίποτα. Σε τι χρειάζεται;

[@user-uz2fz5px1o]

Υπάρχει απλή μέθοδος, το κομπιούτερ

[@muhannawa]

There is another way easier..

[@user-mq8bt7fp2m]

66667

[@user-zh4cn6wo8m]

이렇게 긴 숫자는 계산기가 하면됩니다. 요즘세상에 누가 이런 복잡한 숫자를 수많은 시간 보내면서 낭비합니까? 시간낭비 머리 낭비입니다. 그시간에 더 가치있는 일을 해야 합니다.

[@user-fy5zx4zo6c]

그냥 계산기에 넣고 돌리자