Jeff,
I recommend using a constructor such as DragMath to double check your work hen you come up against something like this. By way of example, the example you wanted to use took only a few seconds to build via dragmath with these results:
$$ \frac{ \sqrt{48} }{ \sqrt{3} } = \frac{ \sqrt{3} \sqrt{16} }{ \sqrt{3} } = \sqrt{16} =4$$
Clicking on the equation after saving will then produce the underlying TeX....