Question

A general wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out ?​

Answer 1

If you want to form a square of 7500 soldiers, the side of the square must be $\sqrt{7500}\approx86.6$ soliders.

But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.

That number is 7396 which when square rooted gives 86 soliders on the side.

Subtract 7396 from 7500 and get how many soliders were left out,

$7500-7396=\boxed{104}$

Hope this helps :)