Question

8647 students were sitting in a lecture room in such a manner that there were as many students in the row as there were rows in the lecture room. How many more students will be required for this arrangement?

Answer 1

Step-by-step explanation:

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Answer 2

$Total \: number \: of \: students = 8647$

$Let \: number \: of \: rows \:in \:the \: lecture$

$hall = x$

$Number \: of \: students \: sitting \: in \:each$

$row = x$

$Total \: students = 8647$

$\implies x \times x = 8647$

$\implies x^{2} = 8647$

$We \:find \; by \:division \:method \:that$

9 | 8647 | 94

×9| 81

_________

183| 547

* ×3| 549

__________

********(-2)

$The \: remainder \: is \: 2$

$This \:means, \: if \:we \: add \: 2 \: to \::8647$

$We \:get \: a \: perfect \: square .$

$\red { Hence, the \: number \: of \:more }$

$\red { students \: required \: for \: above }$

$\red { arrangement } \green { = 2 }$

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