Question

$(1035+x)$ chairs are placed in an auditorium in such way that the number of rows is equal to number of columns. Find the least value of $x$.

Answer 1

$1035+x$ chairs

given rows $=$ columns

Let rows be y

$\Rightarrow y^2=1035+x$

It should be perfect square we should find least value of x

We know it should be greater than ${30}^2=900$.

Now ${31}^2=961$

${32}^2=1024$

${33}^2=1089$

$\therefore$ It should be $1089-1035=54$

Least value of $x=54$.