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.
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
$=\sqrt{5929}=7 \times 11=77$
Hence, in the arrangement, there were 77 rows of students.