Question

If \[7921\] soldiers sat in an auditorium in such a way that there are as many as soldiers in a row as there are rows in the auditorium. How many rows are there in an auditorium?

Answer 1

Hint: Here, in the given question, we need to find the number of rows in an auditorium. We are given that there are as many soldiers in a row as there are rows in the auditorium, which means that the number of rows is equal to the number of soldiers seated in each row. From here we can conclude that the product of the number of rows and number of soldiers seated in each row will be equal to the total number of soldiers. So, we will assume the number of rows is $x$, which is equal to the number of soldiers seated in each row and equate it to the total number of soldiers and find the value of $x$.

Complete step by step solution:
Given,
Total number of soldiers = $7921$
Let the number of rows in an auditorium = $x$
As we know, the number of rows is equal to the number of soldiers seated in each row. Therefore,
Number of soldiers seated in each row = $x$
Total number of soldiers = $x \times x$
$ = {x^2}$
According to the given problem,
${x^2} = 7921$
On taking square root, we get
$ \Rightarrow x = \sqrt {7921} $
$ \Rightarrow x = \sqrt {89 \times 89} $
$ \Rightarrow x = 89$
Therefore, the number of rows in the auditorium = $89$.
So, the correct answer is “89”.

Note: Remember that a positive number has two square roots, one positive and one negative. But here we wrote only positive values because the number of rows can never be negative. The value of the square root can also be determined by using the long division method. We should take care of the calculations so as to be sure of our final answer.