Math olympiad problem a square root without calculator | Geendle
2024 ж. 7 Сәу.
12 230 Рет қаралды
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In this video I solve the square root of a huge number without using a calculator.
#squareroot ,#crossmultiplicationmethod ,#division ,#fraction ,#maths ,#algebra ,#subtraction ,#calculus
Nice solution
Thank you - that was fun!
That was excellent!
I'm so glad for the comment! Thank you verry much, @markgraham2312.
7:12 I do not get it. What am I missing?
Not even Ramanujan would come up with such an ingenius solution.
Thank you my dear!
long division has left the chat
and no one wondering "why would I ever need to solve something like this???" 🤣
You need to become familiar with the estimation method used by math students before calculators were invented. Starting with the decimal point of the number in question, mark the digits of the number in pairs. Then find the largest number squared which will divide the first pair. In this case the number is 6. Six squared = 36 ; subtract from first pair 44-36 = 8 ; Bring down next pair you have 844. Double the number on top(2x6=12_ with a space for the next divisor to produce 844/126 continue this process until you get 66667
Great, my friend! Thanks a lot.
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The another approach to the problem is only by analyzing the square root of 44444888889 1. it must be an 5-digits number (let's ignore for a while the last six digits); 2. the first digit must be < 7 because 7 * 7 = 49 (we must have 444... and so on); 3. the first digit must be > 5 because we never reach the 4 as the first digit of given number; 4. so the first digit must be 6; 5. than the first five digits must be at least 66666 (we must have 444... and so on) 6. but the number is "a little bigger" because our last six digits 7. the last digit is 9, so only 7 makes the last digit 9 (the digit must be > 6) so the answer is: 66667 We can also analyzing in that way (only the even numbers of 4's): √44 = a little more than 6,6 √4444 = a little more than 66,66 √444444 = a little more than 666,666 √44444444 = a little more than 6666,6666 √4444444444 = a little more than 66666,66666 √4444488889 ---> the last digit is 9 so the last digit of the square root must by 7 (not 3, because 3
Fascinating. I'd suggest using commas to separate hundreds, thousands, etc. That way we don't lose track of how many 1's and 9's we have. I'll have to go over it again w my own scratch paper. Very nimble brain work.
Thank you my dear. I'll pay attention to this in the next videos.
Why do it this wy? I did it the old fashioned way in 5 steps.
And me!
Θετω χ=11111 αρα εχω 4444488889=44444.10^5+88888+1=4×.10^5+8χ+1=4χ(99999+1)+8χ+1=4χ(9χ+1)+8χ+1=(6χ)^2+12χ+1=(6χ+1)^2=....=66667
I just found this way kinda cool to do so. Thanks for sharing tour thoughts on this problem my dear.
This is a very nice and short form. Yhanks for sharing my friend.
The video is interesting ; but , as you say the old fashioned way is quicker . It is kind of like turning an arithmetic problem into an algebra problem .
Объясняет как для дурачков, но дурачки-то всё равно не поймут
Tedious and unconvincing!