From the thumbnail, this problem reminds me of a semi-familiar rule about perfect squares of integers that end in "5," namely that the square will be a "rectangular" number followed by "25." A rectangular number (R.N.) is just the product of two consecutive integers, and the R.N., n(n+1), that appears in that square, uses as "n" whatever came before the "5" in the number being squared. So for instance, for 45, you have n=4, and form n(n+1) = 4·5 = 20, so 45² = 2025. For 85, n=8, n(n+1) = 8·9 = 72, so 85² = 7225. Etc. In the current problem, you might see that shortening the radicand to 4225, you may see that 42 = 6·7, so 4225 = 65². Then you might wonder whether you could lengthen the "42" by replicating each of its digits, and ask whether the following pattern holds: 25 = 5² 4225 = 65² 442225 =? 665² 44422225 =? 6665² 4444222225 =? 66665² It isn't immediately obvious that it should, but it so happens that it does. And while that won't help on the test this problem appeared in, unless you make the bold (& lucky!) assumption that it works, this fact begs another, related question: Can you get a similar pattern to work with other squares-ending-in-5? Turns out you can - some such patterns work; others don't. Can you figure out which ones do and which ones don't, and why? Fred
Even if i know all the mathematical formulae in the world, who the hell would think of breaking down such a huge number into the correct components that would fit into a formula ?
no offense intended, but breaking problems down into simpler components is basic problem-solving and a skill you learn in most STEM fields. it becomes almost a reflex after you have done it enough
and it shows how 'little' actual knowledge is needed to solve such a 'huge' problem at first sight...impressive though I have to agree on the fact that repetition helps a lot in seeing 'creative' ways 😊
Use square root long division method, much simpler with a guaranteed result. While a result was eventually found using the method described here this could not be predicted at the start.
I'm a bit rusty on pencil and paper square roots, but it would be my first go-to idea. Although the starting number is weird enough that I might see the patterns he saw in it.
65x65=4,225 665x665=442,225, hence 25 is square of 5 and for every 4 or 2 is coming from 6, in this question 44442222 is from 6666 and the final answer is 66665
@sanchellewellyn3478 It was obvious to me because it should be ended with 5 but started with 7 is too big, and 5 is too small. The only doubt was the answer doesn't necessarily an integer. But it's worth spending a few mins to check this trick.
What you do is this: 4'444'222'225 = 39'998'000'025/9 = (40'000'000'000-2'000'000+25)/9 = (200'000-5)^2/9, hence square root is 199'995/3 = 66'665. In a somewhat extended way. 😉
Whenever a perfect square ends in 25 it means it’s the square of xyz…5 and the digits of the square before the 25 will always be xyz… into xyz… + 1 for example let’s say the square of 35 it will be 3*(3+1) and 25 at the end that is 3*4=1225 you can try with any number it works like 1815 squared will be 181*182 and 25 that is 3294225 so luckily here since it’s ending with 25 just remove the 25 and write the left out number as x*(x+1) and from there we can find x and and add 5 at the end for the answer … this can easily be proved from basic identities
Solution 66665 in 2 seconds: given) 4444222225 step 1) 4444 2222 25 step 3) 4444 + 2222 = 6666 step 4) 25 >> square root = 5 step 5) solution: 6666 add the 5 >>> 66665 ... took much longer to write this down than to calculate it. NB: of course this is a special case, selected by OP for this very reasonn ;)
Nicely made. Two notes: Why do people think that kids at primary school should not develop a fundamental number knowledge? And: I thought it impossible and a kind of miracle when I started math studies. After having been through the " land of thousands math tasks" I somehow found it faisable.
Разложить на множители количество сотен числа под корнем. Получить 6666х6667. Т.е. 66665 в квадрате - искомое число под корнем. Свойство: (10а + 5)² = 100а(а+1)+25, где а - число десятков. 75²=100*7*(7+1)+25=5625.
a(a+1)*100+25=(10a)^2+100a+25=(10a)^2+2*10*5a+25=(10a+5)^2, 44442222=1111*40002=1111*2*20001=1111*2*3*6667=6666*6667=6666*(6666+1), then 4444222225=44442222*100+25=6666*(6666+1)*100+25=(10*6666+5)^2=66665^2
By inspection, the number in question begins with 6 and ends with 5. Ignore the end 25, and just consider 44442222. Factoring this 44442222 will give you the answer. 44442222= 40002 * 1111 = 6*6667*1111. The answer is 66665 (as we know the structure of numbers ending with 5)
@@MAS1234Pyou two are talking about the same thing. He describes more complete solution by multiplying 100+25. The one from video is too complicated and unpredictable through braking down the numbers which will costs much more time to get the solution
@@songlin1506 I don't think my method is the same as the video. My method is based on the knowledge of the square of a number ending with 5 is ending with 25 and with a special structure.
You solved the square root by doing several collections but I won't do the particular division. I'll do it on a piece of paper and write it down for you.
I dont believe this is a question from any university admission, no student with normal school knowledge would ever make such a long calculations, basically its just guessing how to write numbers differently so that at the end its in a convenient form. Then i can also guess some number and square it to see if it gives the desired result. and if just one digit of the original number is changed the whole calculations would not work anymore.
I worry about you. This question can be answered with fundamentals knowledge, you don't even need high school knowledge to crack this. The thing is this questions are meant to test how much do you exercise. Cos anyone that has done thousands of little math exercises knows also about several tricks like this and in your head you would have already come to the conclusion that how you should factor that number in 10 seconds before starting to demonstrate. It is the correct notation of demonstration that takes time.
@jacypr , just for information i have a master degree in mathematics, wrote my master thesis on lattice problems in cryptograhy. However I cannot calculate such problems, never needed this in university or in a real life job. If you say these kind of specific calculation problems should show how much people exercise math problems, well then you exclude all the people who dont, i guess around 95%. You would only get the people who likely have no social life but can rewrite numbers. Maybe universities want to get exactly those people, i dont know.
I like the alternative approach (thinking outside the box) here but does it not rely on a perfect square being at the root for the identity to be useful.
Very clever, but intrinsically useless. One can follow the algebraic manipulation BUT what was the thought process that gets you here? Now that would be useful. No one - except perhaps a Ramanujan - would immediately ‘see’ those manipulations. There is surely some recognisable attributes of the original number that takes the thought process down this route. What is that? What numerical techniques would lead you to think in this way? This reminds me of several examples where children have solved weird mathematical puzzles that their parents cannot only to discover that the children had recently been taught the solution tricks in a previous lesson and are on the look-out for puzzles of this kind. Come on, give an EXPLANATION 🧐
The intuition I used is that the number has 10 digits, so the solution is likely to have 5 digits. I don't know if this violates the 'no computations' rule, but you can quickly see that the answer is somewhere between 60,000 and 70,000 as those will yield 36 * 10^8 and 49 * 10^8, respectively, bracketing our target. Approaching from the lower bound, if you try 66,000, you will see it becomes 36 * 10^8 + 2 * 36 * 10^7 + 36 * 10^6 = 4356 * 10^6. If we extend this pattern further, then we will get some additive spill over that will push even these higher order digits closer to our target. The answer obviously ends in 5. So, try 66,665 and it works.
Total waste of time for practical work. In the real world (lacking a calculator) we could estimate the square root with trial and error...and do better with a slide rule or log tables. Given that the number is approximately 44.4 x 10⁸, I can estimate that square root is around 6.7 x 10⁴....within 1/2 of one percent of the exact answer.
YeH....ok. Well, I dod pretty well not going to Harvard & was lazy enough to put this number into my calculator which got the same result in about 5 seconds versus 20 minutes and a lot of convoluted mathematics. While those who are doing this manually or wasting time, I'm out picking up chicks and hanging out on the beach with my HP 55 II (ala - "The Dude').
What a nightmare you mde there, literally fed up. Its a divisibility question, ends with 5 so divisible by 25 too, divide by 25 then look for other prime numbers with divisibility method. Will take 2minutes. We all need a therapy after seeing this 😆
Not 2 mn, as explained the other factors are 67 and 199, you have to eliminate quite a number of possibilities before (yes, not all, Fermat Little Thoerem etc, but still);
12:59 extremely boring and complicated and meaningless efforts. Usually we watch clips which are useful and educative. Unfortunately your work didn’t give that impression with a 14-minutes clip
It is a meaningless expression. There is no divisor in this division expression. Solve 52 for me... it's a statement, not a question. Nice try, but failure at a meaningful video. Good luck.
Gosh I hope you are not a teacher because you did not explain what you were doing and why. If you are a Professor I understand because they do not actually teach.
it's like you ask your government to calculate for you taxes bills and your pension. maybe they are wrong, however if you know the basic calculations at least you have a way to get your numbers correct. Also d'ont overestimate your calculator. In principle everything goes fine but in the past even a Computer like a Pentium used in Accountancy and everywhere git the F0 Bug! and some old conputers the Millennium bug . Ok you can use your cakculator now but keep in mind that in some way is good to devrlop analytical thinking.
What a bunch of ridiculous nonsense! Just find the square root! Is it that you don't know how? 😮💨 First, separate every 2 digits, from the right side: √44 44 22 22 25. Then, find nearest square to 44: 6² = 36 Subtract 36 from 44 Bring down next 2 digits. 6 √44 44 22 22 25. -36 ⬇️ ----⬇️ 844 Now begins the repeated process: double the answer so far, 6 ×2 = 12, put a digit after the result 12🔳. That digit is the same as the next answer digit. 6 🔳 √44 44 22 22 25. -36 ---- 12🔳 844 How many times does 12🔳 (1 hundred twenty something) go into 844? About 6... 126 × 6, subtract from 844, bring down next 2 digits... 6 6 √44 44 22 22 25. -36 ⬇️ ---- ⬇️ 126 844 ⬇️ ×6 =➡️-756 ⬇️ ------ ⬇️ 88 22 Repeat process: 66 × 2 = 132. 132🔳 × 🔳 = 8822 🔳 = 6 6 6 6 √44 44 22 22 25. -36 ⬇️ ---- ⬇️ 844 ⬇️ -756 ⬇️ ------ ⬇️ 1326 8822 ⬇️ ×6=➡️-7956 ⬇️ ------- ⬇️ 866 22 Repeat: 6 6 6 6 √44 44 22 22 25. -36 ⬇️ ---- ⬇️ 844 ⬇️ -756 ⬇️ ------ ⬇️ 8822 ⬇️ -7956 ⬇️ ------- ⬇️ 13326 86622 ⬇️ ×6 = - 79956 ⬇️ ---------- ⬇️ 6666 25 Repeat: 6 6 6 6 5 √44 44 22 22 25. -36 ---- 844 -756 ------ 8822 -7956 ------- 86622 - 79956 ---------- 133325 666625 ×5 = -666625 ---------- 0 Answer = 66,665 If you know how to do square roots, it's easily done in under a minute. This 13+ minutes of utter BS in the video was ridiculous.
I feel terrible did not under stand,,, like many things were missed not explained,,,, most people over 99 percent cant do this strange rules... I thought numbers could be canceled easier and you add exponents
How come majority of Math content creators with questionable credibility copy from me and you viewers rush to their comments section glorifying them for something they did not make?
From the thumbnail, this problem reminds me of a semi-familiar rule about perfect squares of integers that end in "5," namely that the square will be a "rectangular" number followed by "25."
A rectangular number (R.N.) is just the product of two consecutive integers, and the R.N., n(n+1), that appears in that square, uses as "n" whatever came before the "5" in the number being squared.
So for instance, for 45, you have n=4, and form n(n+1) = 4·5 = 20, so 45² = 2025.
For 85, n=8, n(n+1) = 8·9 = 72, so 85² = 7225.
Etc.
In the current problem, you might see that shortening the radicand to 4225, you may see that 42 = 6·7, so 4225 = 65².
Then you might wonder whether you could lengthen the "42" by replicating each of its digits, and ask whether the following pattern holds:
25 = 5²
4225 = 65²
442225 =? 665²
44422225 =? 6665²
4444222225 =? 66665²
It isn't immediately obvious that it should, but it so happens that it does. And while that won't help on the test this problem appeared in, unless you make the bold (& lucky!) assumption that it works, this fact begs another, related question:
Can you get a similar pattern to work with other squares-ending-in-5?
Turns out you can - some such patterns work; others don't.
Can you figure out which ones do and which ones don't, and why?
Fred
Thanks for sharing your feedback and I'm glad you found it helpful 🙏🤩💕🥰
Please take a long process and make more thought-provoking questions like this, sir. Thank you🎉
Even if i know all the mathematical formulae in the world, who the hell would think of breaking down such a huge number into the correct components that would fit into a formula ?
It's a matter of intuition, I think. But somehow, this seems obvious.
It is called routine how to solve exercises like this.
no offense intended, but breaking problems down into simpler components is basic problem-solving and a skill you learn in most STEM fields. it becomes almost a reflex after you have done it enough
and it shows how 'little' actual knowledge is needed to solve such a 'huge' problem at first sight...impressive though I have to agree on the fact that repetition helps a lot in seeing 'creative' ways 😊
Cause all the mathematical formulae in the world go where sun never shines 😂. You gotta see the beauty of algebra, that's what it's all about.
Only that the number under the square root has to be "pre-selected" to use this elegant algebraic trick
Use square root long division method, much simpler with a guaranteed result. While a result was eventually found using the method described here this could not be predicted at the start.
You are right. It can take hours to find the right path as described
I'm a bit rusty on pencil and paper square roots, but it would be my first go-to idea. Although the starting number is weird enough that I might see the patterns he saw in it.
I thinked in this too
65x65=4,225
665x665=442,225, hence 25 is square of 5 and for every 4 or 2 is coming from 6, in this question 44442222 is from 6666 and the final answer is 66665
from 2/9*(10^n-1)*(2*10^n+1)
we get ⅔(10^n-1)*(⅔(10^n-1)+1)
Now that's a nice trick, if you can spot it. :)
@sanchellewellyn3478 It was obvious to me because it should be ended with 5 but started with 7 is too big, and 5 is too small. The only doubt was the answer doesn't necessarily an integer. But it's worth spending a few mins to check this trick.
What you do is this:
4'444'222'225 = 39'998'000'025/9 = (40'000'000'000-2'000'000+25)/9
= (200'000-5)^2/9, hence square root is 199'995/3 = 66'665.
In a somewhat extended way. 😉
4.4¹⁰+2.2⁶+25=2/3¹⁶+25 ummmm wt????? Never mind
Too many redundant steps. How much time was given for this problem?
Whenever a perfect square ends in 25 it means it’s the square of xyz…5 and the digits of the square before the 25 will always be xyz… into xyz… + 1 for example let’s say the square of 35 it will be 3*(3+1) and 25 at the end that is 3*4=1225 you can try with any number it works like 1815 squared will be 181*182 and 25 that is 3294225 so luckily here since it’s ending with 25 just remove the 25 and write the left out number as x*(x+1) and from there we can find x and and add 5 at the end for the answer … this can easily be proved from basic identities
Solution 66665 in 2 seconds:
given) 4444222225
step 1) 4444 2222 25
step 3) 4444 + 2222 = 6666
step 4) 25 >> square root = 5
step 5) solution: 6666 add the 5 >>> 66665
... took much longer to write this down than to calculate it.
NB: of course this is a special case, selected by OP for this very reasonn ;)
Great! That's neat and nice! Thank you very much.
I'm happy you enjoyed it! I'm glad you found it useful 🙏🤩💕💯🔥💪
Nicely made.
Two notes: Why do people think that kids at primary school should not develop a fundamental number knowledge?
And: I thought it impossible and a kind of miracle when I started math studies. After having been through the " land of thousands math tasks" I somehow found it faisable.
Now, if someone does not want to use a canned square root manual method, can reach the exact same conclusion by explicit analysis.
Call xEn = x.10^n
So
abcde = aE4 + bE3 + cE2 + dE1 + eE0
(abcde)^2 = (a^2)E8 + (b^2)E6 + (c^2)E4 + (d^2)E2 + (e^2)E0
+ (2.a.b)E7 + (2.a.c)E6
+ (2.a.d)E5 + (2.a.e)E4+ (2.b.c)E5 + (2.b.d)E4
+ (2.b.e)E3 + (2.c.d)E3 + (2.c.e)E2
+ (2.d.e)E1
= (a^2)E8 + (b^2)E6 + (c^2)E4 + (d^2)E2 + (e^2)E0
+ (20.a.b)E6 + (2.a.c)E6
+ (20.a.d)E4 + (2.a.e)E4+ (20.b.c)E4 + (2.b.d)E4
+ (20.b.e)E2 + (20.c.d)E2 + (2.c.e)E2
+ (20.d.e)E0
= (a^2)E8 + (b^2+20.a.b+2.a.c)E6 + (c^2+20.a.d+20.b.c+2.a.e+2.b.d)E4 + (d^2+20.b.e+20.c.d+2.c.e)E2 + (e^2+20.d.e)E0
= 4444222225 = 44 44 22 22 25
= 44E8 + 44E6 + 22E4 + 22E2 + 25E0
we look at the E8 term (ie, 10^8). We find the maximum a that satisfy
a^2
That's a very clever and detailed analysis! 💪🔥I'm glad you found an alternative method! 💯
I'm a math major here.
Tops in the nation.
But I can say that this problem is exactly why God created calculator.
It's not a problem, it's a statement. This is a trick question. The answer is there is no answer because it is simply a number. Solve 125 for me...
I am from India, in 12th standard and as a jee student solved it easily it was too easy 😊
I'm glad you found it helpful! 💯 It's great that you're studying hard for your exams! 🙏
44442222=2222*20001=6666*6667
√4444222225=66665
In general: √4..42..225=6..65
Well done very tidy 👌
Thanks 👍💯😊🤩
Разложить на множители количество сотен числа под корнем. Получить 6666х6667. Т.е. 66665 в квадрате - искомое число под корнем. Свойство: (10а + 5)² = 100а(а+1)+25, где а - число десятков. 75²=100*7*(7+1)+25=5625.
a(a+1)*100+25=(10a)^2+100a+25=(10a)^2+2*10*5a+25=(10a+5)^2, 44442222=1111*40002=1111*2*20001=1111*2*3*6667=6666*6667=6666*(6666+1), then 4444222225=44442222*100+25=6666*(6666+1)*100+25=(10*6666+5)^2=66665^2
By inspection, the number in question begins with 6 and ends with 5.
Ignore the end 25, and just consider 44442222. Factoring this 44442222 will give you the answer. 44442222= 40002 * 1111 = 6*6667*1111. The answer is 66665 (as we know the structure of numbers ending with 5)
@@MAS1234Pyou two are talking about the same thing. He describes more complete solution by multiplying 100+25.
The one from video is too complicated and unpredictable through braking down the numbers which will costs much more time to get the solution
@@songlin1506 I don't think my method is the same as the video. My method is based on the knowledge of the square of a number ending with 5 is ending with 25 and with a special structure.
I do it starting from 6xxxx5 because of 4×10^9 and final 5 and then try different solutions for the cifers.
You solved the square root by doing several collections but I won't do the particular division. I'll do it on a piece of paper and write it down for you.
I did the algorithm to extract square roots by hand... Took a little bit under 5 mins.
I did the same but shortened the work by factoring out 5s. I used Newton's iteration for the square root and multiplied by 5.
thank you very much，sir
You're welcome! 🎉🎁🥳🎄Thanks for your support and feedback! 💯🙏🤩💕
I dont believe this is a question from any university admission, no student with normal school knowledge would ever make such a long calculations, basically its just guessing how to write numbers differently so that at the end its in a convenient form. Then i can also guess some number and square it to see if it gives the desired result. and if just one digit of the original number is changed the whole calculations would not work anymore.
But most of mathematical tasks are intentionally prepared just for such calculations
I worry about you. This question can be answered with fundamentals knowledge, you don't even need high school knowledge to crack this. The thing is this questions are meant to test how much do you exercise. Cos anyone that has done thousands of little math exercises knows also about several tricks like this and in your head you would have already come to the conclusion that how you should factor that number in 10 seconds before starting to demonstrate.
It is the correct notation of demonstration that takes time.
@jacypr , just for information i have a master degree in mathematics, wrote my master thesis on lattice problems in cryptograhy. However I cannot calculate such problems, never needed this in university or in a real life job. If you say these kind of specific calculation problems should show how much people exercise math problems, well then you exclude all the people who dont, i guess around 95%. You would only get the people who likely have no social life but can rewrite numbers. Maybe universities want to get exactly those people, i dont know.
Closer..the fact is there is no solution, it is simply a number. Solve 367 for me.
bravo!
Try prime number factorization
Super
Thanks🥂
🎉prefiro tirar a raiz no modo antigo.
I like the alternative approach (thinking outside the box) here but does it not rely on a perfect square being at the root for the identity to be useful.
I'm glad you're noticing the nuances of this approach! 💪
❤️❤️❤️
Voll interessant
Very clever, but intrinsically useless. One can follow the algebraic manipulation BUT what was the thought process that gets you here? Now that would be useful. No one - except perhaps a Ramanujan - would immediately ‘see’ those manipulations. There is surely some recognisable attributes of the original number that takes the thought process down this route. What is that? What numerical techniques would lead you to think in this way?
This reminds me of several examples where children have solved weird mathematical puzzles that their parents cannot only to discover that the children had recently been taught the solution tricks in a previous lesson and are on the look-out for puzzles of this kind.
Come on, give an EXPLANATION 🧐
The intuition I used is that the number has 10 digits, so the solution is likely to have 5 digits. I don't know if this violates the 'no computations' rule, but you can quickly see that the answer is somewhere between 60,000 and 70,000 as those will yield 36 * 10^8 and 49 * 10^8, respectively, bracketing our target. Approaching from the lower bound, if you try 66,000, you will see it becomes 36 * 10^8 + 2 * 36 * 10^7 + 36 * 10^6 = 4356 * 10^6. If we extend this pattern further, then we will get some additive spill over that will push even these higher order digits closer to our target. The answer obviously ends in 5. So, try 66,665 and it works.
Asyik juga nih
Проще подбором. Очевидно что число 6XXX5. Остаётся слева направо подобрать недостающие цифры.
I guess nobody teaches how to calculate a square root manually in the USA anymore. It's not difficult:
4444222225
44 6*6 = 36
36
844 126*6 = 756
756
8822 1326*6 = 7956
7956
86622 13326*6 = 79956
79956
666625 133325*5 = 666625
666625
0
Answer: 66665
Total waste of time for practical work.
In the real world (lacking a calculator) we could estimate the square root with trial and error...and do better with a slide rule or log tables.
Given that the number is approximately 44.4 x 10⁸, I can estimate that square root is around 6.7 x 10⁴....within 1/2 of one percent of the exact answer.
It is much more reliable to use the formal decomposition method, given limited time for exams😅.
Thanks for sharing your perspective! 🙏I'll keep that in mind for future videos! 😉 💯
what is "fata lita nas"?
its good if you know the exact result first.
Warum nicht gleich händisch ausrechnen, da gibt es eine einfache Regel zum Wurzelziehen, da dauert diese Rechnung etwa 1 Minute.
There is no calculation, it is simply a number. Where is the divisor?
Я не зеленый, но даже мне становится не по себе, когда он использует столько строк для сворачивания квадрата разности.
Tanks for watching
Thanks for your support! 🔥🙏🤩💕I appreciate you watching! 💯🥰💕
It is 320. It took me 3 minutes. No calculator. 4x4 square root is. Just keep going until 25 square root is 5. Soooooo simple
I’m glad you found it helpful! 💯🙏🤩💕Thanks for sharing your method! 🚀
@@ruperttristanblythe7512 I was trying to be nice. This one is so obvious.
Genial
I didn't look at all 101 comments, but shouldn't the answer be ±66665?
LOL "without calculating"
OK but, if it takes you this long to do one problem on the exam, I don't think you're getting into Harvard...
These are the type of videos required to train AI💪🥂
35² = 30x40+25
995² = 990x1000+25 = 990025
so √(4444222200+25)
44442222 = 1111x2x3x6667
= 6666 x 6667
√(4444222200+25)
= √(66660x66670 + 25)
= √66665²
= 66665
The bigger question is... how big is that never-ending sheet of paper?!!!
Multiple pages 🥂🔥💯
What is the value of solving this?
Call it 45 billion. 70kx70k gets you in the ball park.
Excaty like who's gonna miss a few hundred billions or is it billion?? Either way good call
Qué suena de fondo? El Muhecin? 🫣
I know it's 66,665
YeH....ok. Well, I dod pretty well not going to Harvard & was lazy enough to put this number into my calculator which got the same result in about 5 seconds versus 20 minutes and a lot of convoluted mathematics.
While those who are doing this manually or wasting time, I'm out picking up chicks and hanging out on the beach with my HP 55 II (ala - "The Dude').
Would have been much faster to break the number in prime factors.
Not really, the factors are 5 (ok), but then 67 and 199... But of course it is more systematic.
I think those answer is not wrong, but not true cause root. Exactly plus minus if the rule of root.
14 minutos para una raiz cuadrada?
What a nightmare you mde there, literally fed up. Its a divisibility question, ends with 5 so divisible by 25 too, divide by 25 then look for other prime numbers with divisibility method. Will take 2minutes. We all need a therapy after seeing this 😆
I'm glad you found a faster method! I was trying to demonstrate a different approach for understanding the problem. 👍🥂
Not 2 mn, as explained the other factors are 67 and 199, you have to eliminate quite a number of possibilities before (yes, not all, Fermat Little Thoerem etc, but still);
@@catherineg.1831 well its 2mins for me. after dividing by 25 its all becoming a test of small intervals. you use other tactics as well
An MIT janitor could do that problem. Easy. How 'bout them apples!
Dang. I was hoping the answer was 42.
Why we need to learn this when we have Ai?😂😂😂
To produce AI you need
But at the last step you did guesswork.
Very clever
Thanks for your support and feedback 💯🙏🙏💡✅💪
12:59 extremely boring and complicated and meaningless efforts.
Usually we watch clips which are useful and educative. Unfortunately your work didn’t give that impression with a 14-minutes clip
Very lengthy .
I made this video longer for deeper understanding! 🥂. Very useful for machine learning and artificial intelligence models
just long division bro
I dont see any real application of this
❤
Or.. 4+2, 4+2, 4+2, 4+2 |~25
=66665
Lol
It is a meaningless expression. There is no divisor in this division expression. Solve 52 for me... it's a statement, not a question. Nice try, but failure at a meaningful video. Good luck.
This is not math. You need help
Gosh I hope you are not a teacher because you did not explain what you were doing and why. If you are a Professor I understand because they do not actually teach.
Wrong calculation😂 of my wasted time
This is ridiculous. Absolute nonsense.
Stupid and time wasting. Ask Ai.
Useless.... So why we invented calculator??
it's like you ask your government to calculate for you taxes bills and your pension. maybe they are wrong, however if you know the basic calculations at least you have a way to get your numbers correct.
Also d'ont overestimate your calculator. In principle everything goes fine but in the past even a Computer like a Pentium used in Accountancy and everywhere git the F0 Bug! and some old conputers the Millennium bug . Ok you can use your cakculator now but keep in mind that in some way is good to devrlop analytical thinking.
개평법이용
또는 6667×6666=
444442222이므로
66665²
What a bunch of ridiculous nonsense!
Just find the square root!
Is it that you don't know how?
😮💨
First, separate every 2 digits, from the right side:
√44 44 22 22 25.
Then, find nearest square to 44: 6² = 36
Subtract 36 from 44
Bring down next 2 digits.
6
√44 44 22 22 25.
-36 ⬇️
----⬇️
844
Now begins the repeated process: double the answer so far, 6 ×2 = 12,
put a digit after the result 12🔳.
That digit is the same as the next answer digit.
6 🔳
√44 44 22 22 25.
-36
----
12🔳 844
How many times does 12🔳 (1 hundred twenty something) go into 844? About 6...
126 × 6, subtract from 844, bring down next 2 digits...
6 6
√44 44 22 22 25.
-36 ⬇️
---- ⬇️
126 844 ⬇️
×6 =➡️-756 ⬇️
------ ⬇️
88 22
Repeat process:
66 × 2 = 132.
132🔳 × 🔳 = 8822
🔳 = 6
6 6 6
√44 44 22 22 25.
-36 ⬇️
---- ⬇️
844 ⬇️
-756 ⬇️
------ ⬇️
1326 8822 ⬇️
×6=➡️-7956 ⬇️
------- ⬇️
866 22
Repeat:
6 6 6 6
√44 44 22 22 25.
-36 ⬇️
---- ⬇️
844 ⬇️
-756 ⬇️
------ ⬇️
8822 ⬇️
-7956 ⬇️
------- ⬇️
13326 86622 ⬇️
×6 = - 79956 ⬇️
---------- ⬇️
6666 25
Repeat:
6 6 6 6 5
√44 44 22 22 25.
-36
----
844
-756
------
8822
-7956
-------
86622
- 79956
----------
133325 666625
×5 = -666625
----------
0
Answer = 66,665
If you know how to do square roots, it's easily done in under a minute.
This 13+ minutes of utter BS in the video was ridiculous.
Too late
Just use the 'evolution' method taught before calculators or log tables were developed.
I feel terrible did not under stand,,, like many things were missed not explained,,,, most people over 99 percent cant do this strange rules... I thought numbers could be canceled easier and you add exponents
Don't feel badly; I have a degree in math, and I could not understand THIS problem as well. However, I am able to solve most of his Harvard problems.
So, we will never accepted by harward😁
1% of people have 99% of money.
@@ivandemydov9702 that %1 can not solve this either.
Just rewatch slowly he explains everything
Do not make ANY more videos on YT until : 1- you know how to teach a subject and 2- you can speak english better.
How come majority of Math content creators with questionable credibility copy from me and you viewers rush to their comments section glorifying them for something they did not make?
Ma va da via al cul