Floor summation

Let S denote the expression given below:

$\sum _{ x=1 }^{ 224 }{ \left\lfloor \sqrt { x } \right\rfloor }$

then if value of S can be expressed as ${ \alpha }^{ \delta }{ \beta }^{ \mu }{ \gamma }^{ \lambda }$

then value of $\alpha +\beta +\gamma +\delta +\mu +\lambda \\$ is

where $\alpha ,\beta ,\gamma$ are prime numbers