Three-fifth of the square of a certain number is 126.15. What is the numbers ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let the number be }}x \cr & {\text{Then,}} \cr & \Leftrightarrow \frac{3}{5}{x^2} = 126.15 \cr & \Leftrightarrow {x^2} = \left( {126.15 \times \frac{5}{3}} \right) \cr & \Leftrightarrow {x^2} = 210.25 \cr & \Leftrightarrow x = \sqrt {210.25} \cr & \Leftrightarrow x = 14.5 \cr} $$