Out of 745 students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if 16 students were left out after the arrangement.

Let the number of columns be $x$.

The number of rows = the number of columns = $x$

Students arranged in P.T. display = 745 - 16 = 729

Hence,

$x \times x = 729\\[1em] ⇒ x^2 = 729\\[1em] ⇒ x = \sqrt{729}\\[1em] ⇒ x = \sqrt{27 \times 27}\\[1em] ⇒ x = 27$

Hence, the number of rows = 27.