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Question
A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after arrangement.
Solution
Since 71 students were left out, there are only 5929 (6000 \[-\]71) students remaining.
Hence, the number of rows or columns is simply the square root of 5929.
Factorising 5929 into its prime factors:
5929 = 7\[\times\]7\[\times\]11\[\times\]11
Grouping them into pairs of equal factors:
5929 = (7 x 7) x (11 x 11)
The square root of 5929
=`sqrt(5929)=7xx11=77`
Hence, in the arrangement, there were 77 rows of students.
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