Question

64516 people are sitting in an auditorium in such a way that there are as many people in a row as there are rows in the auditorium. How many rows are there in the auditorium?​

Answer 1

Answer:

There are 508 rows in the auditorium.

Step-by-step explanation:

Let there be 'a' rows in the auditorium.

Since the number of students in a row is same as the number of rows in the auditorium

.°. No. of students in a row = a

=> No. of students in 'a' rows = a×a = a^2

It is given that the total number of students in the auditorium = 64516

.°. a^2 = 64516

=> a = √64516

4 ∣ 64516

127 ∣ 16129

∣ 127

⇒a= (4× 127 × 127)

[By prime factorisation]

⇒a= 4 × 127 [Taking one factor in each pair]

=> a= 508

Hence, there are 508 rows in the auditorium.