Question

There are $2401$ students in a school. A P.T teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columns. Find the number of rows.
A. $42$
B. $44$
C. $49$
D. $50$

Answer 1

Here we must know that when we have $m$ students in the row and $n$ students in the column then the total number of students standing is equal to the product of the number of students in rows and columns which is given by $mn$.

Complete Step by Step Solution:
Here we are given that there are $2401$ students in a school and the P.T teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columns.
As the number of rows and columns are equal so we can let the number of rows and number of columns be any variable.
Number of rows$=$Number of columns$= x$
Now we know that if we have $m$ students in the row and $n$ students in the column then the total number of students standing is equal to the product of the number of students in rows and columns which is given by $mn$.
So as here we are given that the number of rows and columns are equal. So we can say that as they are equal to $x$.
So total students will be
$= \left( {{\text{number of rows}}} \right)\left( {{\text{number of columns}}} \right) \\\ = \left( x \right)\left( x \right) = {x^2} \\\$
We are also given that a total of $2401$ students are there. Hence we can equate ${x^2}$ and $2401$.
${x^2}$ $= 2401$
Now we can solve for $x$ and get:
$x = \sqrt {2401} = \sqrt {\left( 7 \right)\left( 7 \right)\left( 7 \right)\left( 7 \right)} = \left( 7 \right)\left( 7 \right) = 49$
Hence we get that there are $49$ rows as well as columns.

Hence option C) is the correct result.

Note:
Here the student can also be given that there are twice as many rows as columns then we can let the columns as $x$ and rows will be $2x$
Then accordingly we would say that $\left( x \right)\left( {2x} \right) = 2401$ and solve for $x$