# 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.