Question

An army officer wishes to arrange $4770$ soldiers in the form of a square. After arranging he finds that $9$ soldiers are left out. Find the number of soldiers in each row.

Answer 1

Given :

Total number of soldiers $=4770$

Number of soldiers left out $=9$

So, number of soldiers to be arranged in square $=4770-9=4761$

Let the number of rows be $x$

so, the number of columns also be $x$

Now, Soldiers are arranged in a square shape, so,

Total number of soldiers $=$number of rows $\times$ number of columns

$$\begin{gathered} \Rightarrow 4761=x\times x \\ \Rightarrow x^2=4761 \\ \Rightarrow x=\sqrt{4761} \\ \Rightarrow x=69 \end{gathered}$$

Hence, there will be $69$ soldiers in each row.