A school wants the smallest number of students (more than 100) that can be arranged BOTH in rows of 24 and in a perfect square formation (rows = columns). Find that smallest number of students and the side of its square formation.

Question

Accepted Answer

144 students, side 12. The number must be a multiple of 24, a perfect square and more than 100. 24 = 2^3 x 3, so a perfect-square multiple needs an even power of every prime: 2^4 x 3^2 = 144 = 12^2, and 144 = 24 x 6 is indeed a multiple of 24. 144 > 100, so it is the smallest such number, with side √144 = 12.

A school wants the smallest number of students (more than 100) that can be
arranged BOTH in rows of 24 and in a perfect square formation
(rows = columns). Find that smallest number of students and the side of
its square formation.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Finding Square Roots practice

A school wants the smallest number of students (more than 100) that can bearranged BOTH in rows of 24 and in a perfect square formation(rows = columns). Find that smallest number of students and the side ofits square formation.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Finding Square Roots practice

A school wants the smallest number of students (more than 100) that can be
arranged BOTH in rows of 24 and in a perfect square formation
(rows = columns). Find that smallest number of students and the side of
its square formation.