Question

An army officer arranged his group of 2300 Soldiers in a square and, found that 4 Soldiers were short. Find the number of the rows.​

Answer 1

SOLUTION

GIVEN

An army officer arranged his group of 2300 Soldiers in a square and, found that 4 Soldiers were short.

TO DETERMINE

The number of the rows.

EVALUATION

Let the number of the rows = n

Since it forms a square

So number of columns = n

Now it is given that army officer arranged his group of 2300 Soldiers in a square and, found that 4 Soldiers were short

Since 4 Soldiers were short

So by the given condition

$\displaystyle \sf{ {n}^{2} - 4 = 2300 }$

$\displaystyle \sf{ \implies {n}^{2} = 4 + 2300 }$

$\displaystyle \sf{ \implies {n}^{2} = 2304 }$

$\displaystyle \sf{ \implies n = \sqrt{2304 }}$

$\displaystyle \sf{ \implies n = 48}$

FINAL ANSWER

The number of the rows = 48

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Answer 2

$\underline{ \red{ \rm SOLUTION \: \: : }}$

Let the number of the rows = x

Since it forms a square

So number of columns = x

Now it is given that army officer arranged his group of 2300 Soldiers in a square and, found that 4 Soldiers were short.

Since, 4 Soldiers were short

So by the given condition,

$\rm➻ \: \: {x}^{2} - 4 = 2300$

$\rm➻ \: \: {x}^{2} = 2300 + 4$

$\rm➻ \: \: {x}^{2} = 2304$

$\rm➻ \: \: x = \sqrt{2304}$

$\rm➻ \: \: \orange{\boxed{\color{green}{ \colorbox{orange}{x = 48}}}}$

There are 48 rows.