An army of soldiers of 23750 soldiers had to stand in equal rows and coloums . Is it possible to do so? If not how many more soldiers are needed to do so. Find the number of soldiers in each row
not possible or else 23750 would have to be a perfect square.
√23750 is 154.11..
so the next perfect square would have to be 155^2 or 24025 soldiers
So they would need 24025-23750 or 275 more soldiers
@mathhelper
24025 - 23075 = ????
Glad you appreciate my many replies to your problems over the last few weeks by pointing out an obvious typo.
@ mathhelper
And we got 950 ..
AM I right or wrong dear???
And last one
Find number of soldiers in each row??
We have to show square root of ???
Kindly help as I am not able to solve last part
@mathhelper
@oobleck
155^2 = 24025
To determine if it is possible to arrange the soldiers in equal rows and columns, we need to find the factors of the total number of soldiers.
The factors of 23750 are: 1, 2, 5, 10, 25, 50, 125, 250, 475, 500, 625, 1250, 2375, and 4750.
To have an equal number of soldiers in each row, we need at least two soldiers in each row. So, we'll ignore the factors 1 and 2 for now.
Now, let's check each factor to see if it is possible to arrange the soldiers in equal rows and columns:
- For 5 soldiers in each row: 23750 ÷ 5 = 4750 columns, but this would be too many columns.
- For 10 soldiers in each row: 23750 ÷ 10 = 2375 columns, but this would also be too many columns.
- For 25 soldiers in each row: 23750 ÷ 25 = 950 columns, but this is still too many columns.
- For 50 soldiers in each row: 23750 ÷ 50 = 475 columns, and this is a reasonable number of columns.
Therefore, it is possible to arrange the soldiers in equal rows and columns with 50 soldiers in each row.
To find the number of soldiers in each row, we divide the total number of soldiers by the number of columns: 23750 ÷ 475 = 50 soldiers in each row.
No additional soldiers are needed in this case since an equal arrangement is possible with the existing number of soldiers.