There are 1926 soldiers in a platoon. The commander of the platoon wants to impress the visiting general by arranging his soldiers in such a manner that they are arranged in n rows, and each row has n soldiers. He finds that he cannot do this with the number of soldiers he has. What is the minimum number of soldiers he needs additionally to do this kind of a formation?
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Step by Step Explanation:
- It is given that a platoon has 1926 soldiers. The number of rows and the soldiers in each row is the same.
- We have to find the number of more soldiers that should be there, so that when the commander arranged them, the number of rows and the number of soldiers in each row are same.
That is, the number which should be added to 1926 to make it a perfect square has to be calculated.
- If the square root of 1926 is calculated then the quotient and the remainder is 43 , 77 respectively. It represents that the square of 43 with the sum of 77 is equal to the 1926.
The next number is 44 and 442 = 1936
- Hence the number to be added to 1926 to make it a perfect square = 442 - 1926 = 1936 - 1926 = 10
- Therefore, required number of soldiers is 10.