There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

16

Let the number be m, then the square will be m^2
According to question:
2m = (m/4) + 7
=> 8m = m + 28
=> m = 4

m^2 = 4^2 = 16.

The required square is 16.