Kindly help to solve this question.

At a assembly students are arranged in rows to form a perfect square. In doing so 60 students are left out. If the total number of students is 2364, find the number of students in each row.

Dear Student!

Let the number of students in each row be *n*.

Since the students are arranged in rows to form a perfect square,

∴ Number of rows = *n*

Number of students standing in *n* rows = *n* × *n* = *n*^{2}

Number of students standing in *n* rows + Number of students left out = Total number of students

∴ *n*^{2 }+ 60 = 2364 (Given)

⇒ *n*^{2 }= 2364 – 60 = 2304

Prime factorization of 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

⇒ *n* = 2 × 2 × 2 × 2 × 3

⇒ *n* = 48

Thus, the number of students in each row is 48.

Cheers!

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