Prime factorization is much easier and faster prime factorization of 1111222225 is: 5 x 5 x 59 x 59 x 113 x 113 So, the square root is 5 x 59 x 113 = 33335
for those of us who don't have the squares of integers memorized up to 33335^2, (there must be a FEW of us) do you have a different technique to suggest ?
of course we could always fall back on longhand square root, that we all learned in 8th grade. a lot of comments here, in case your memory of 8th grade is dim. example: sqrt(1522756) 1 2 3 4 ------------------------------------------------------ | 1 52 27 56 // pairs of digits from decimal point out | square root of 1 is 1 ... first digit in result is 1 | 1 // subtract and drop next pair of digits | 52 // at this point partial solution is 1 // next subtrahend is (20*1+d) = (20+d)*d ... 22*2 = 44
Have you compared the time you took to do this with the time it would have taken using the traditional square root calculation method?
Prime factorization is much easier and faster
prime factorization of 1111222225 is:
5 x 5 x 59 x 59 x 113 x 113
So, the square root is 5 x 59 x 113 = 33335
it took you that many steps to find the root. I just use binomial expension technique to find the root. it is a lot easier and quicker.
Thanks for sharing
please show us all the steps of using the binomial expension [sic]
technique to find the sqrt(1111222225)
=(100000+5)/3
=(100000-1+5+1)/3
=(99999+6)/3
=3(33333+2)/3
=33333+2
=33335
😂😂😂
33335
111122225=33335×33335
Root111122225=33335
Is that your decision whithout calculator?
for those of us who don't have the squares of integers memorized up to 33335^2,
(there must be a FEW of us) do you have a different technique to suggest ?
of course we could always fall back on longhand square root,
that we all learned in 8th grade. a lot of comments here, in case
your memory of 8th grade is dim. example: sqrt(1522756)
1 2 3 4
------------------------------------------------------
| 1 52 27 56 // pairs of digits from decimal point out
| square root of 1 is 1 ... first digit in result is 1
| 1 // subtract and drop next pair of digits
| 52
// at this point partial solution is 1
// next subtrahend is (20*1+d) = (20+d)*d ... 22*2 = 44
33335
if you don't show your work, it is not very useful.