a) A battalion of soldiers wanted to have a parade forming a square design with 1,536 soldiers. Is it possible? If not how many more soldiers are needed for this arrangement. b) Find the greatest 4 digit number, which is a perfect square?

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Sherlyn Campos

Mathematics

4 July, 17:42

a) A battalion of soldiers wanted to have a parade forming a square design with 1,536 soldiers. Is it possible? If not how many more soldiers are needed for this arrangement. b) Find the greatest 4 digit number, which is a perfect square?

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Andrew Allen · Answer 1

A square with 1,536 soldiers are not possible, i. e. the square root of 1,536 is about 39.191, which means that 1,536 is not a square a number. In order for it to be a square number, we have to round up 39.191 (because it says "how many more soldiers") to 40 and 40*40=1,600 and 1,600-1,536, so we need 64 more soldiers.

The greatest 4 digit number is simple. If the square root of 10,000 is 100, than, one can assume that because 100-1=99, the resulting answer of 99*99 is less than 10,000, meaning that is is 4 digits. 99*99=9,801.