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Easier method: Square root of any number ending in 5 ends in 5; Square of any number 10n+5 is 100n(n+1) +25; so we just need to factorize 44442222; 44442222= 2222*20001=1111*2*3*6667= 6666*6667; THerefore sq root of the number is 66665
I am not a mathematician, so my approach is kinda stupid.
I looked at the end of the number as realized it can be divided first by 25. So I did, with result of 177768889. As it ended with 9, it might get divided by a square of a prime number ending with 3 or 7. I tested (hardest part of my approach) 7,13,17,23,37,43,47,53 and finally 67, which turned out to fit, leaving 39601. It was close to a square of 200 and could be a square of only a number ending in 1 or 9. So I began the test with 199, and it fitted. Result was 5*67*199
Очень красивое решение. Спасибо большое
You're welcome 😍😍🤩🙏
Answer ends with 5
Find the square root of 44442222 which lies between 6666 and 6667
So answer is 66665
Or
44442222=22(2020101=22+3×673367
=66×101×6667=6666×6667
(a5)^2=a(a+)×100+25
Square root of a(a+1)×100+25=a5
I found out the result by conventional method in 7minutes in10 steps.
May be the university wants to find how strong one is in basic methods.
That's an excellent time, well done!You're exactly right, it's about the process, not the speed.🙏👏💕💯
I have no idea to solve this question, I used a method of calculation to extract the square root.
It requires patience to solve this type of question.
@@superacademy247
Fortunately for the students, no real world root problems are being solved. Even if the numbers in real world problems appear convenient, caution has to be used. Hidden human error is often the dominant error with the only knowledge of the error values being they follow a gaussian curve. (Studies of Human Performance. )
Expression under square root is
4 (10^9+10^8+10^7+10^6) + 2 (10^5+10^4+103+10^2+10) + 5
4 × 10^6 (10^4-1)/9 + 2×10 (10^5-1)/9 +5
{ 4 ×10^10-4 ×10^6+
2 ×10^6-20+45 } /9
(4 × 10^10 -2× 10^6 +25)/9
hence square root is
(2×10^5-5)/3
{ 2 × 10 (10^4-1) +15 }/3
6 × 10 (10^4-1)/9 +5
6 ( 10^4+10^3+10^2+10 ) +5
= 66665