Three eighths of the students of a class opted for visiting an old age home. Sixteen students opted for having a nature walk. The square root of a total number of students in the class opted for tree plantation in the school. The number of students who visited an old age the home is the same as the number of students who went for a nature walk and did tree plantation. Find the total number of student.

Let the total number of students = x

According to the question,

Number of students who visited old age home = 3x/8

Number of students who went for nature walk = 16

Number of students who opted for tree plantation = x

According to the question,

⇒ 3x – 128 = 8x

Squaring both sides:

⇒ (3x – 128)² = 64x

⇒ 9x² + 16384 – 768x = 64x

⇒ 9x² – 832x + 16384 = 0

⇒ 9x² – 576x – 256x + 16384 = 0

⇒ 9x(x – 64) – 256(x – 64) = 0

⇒ (x – 64)(9x – 256) = 0

⇒ x – 64 = 0 or 9x – 256 = 0

x = 64 or x =

So, total number of students = 64