To simplify the radical expression:

$4\sqrt{5} + 9\sqrt{45} + 3\sqrt{75}$

Step-by-Step Solution:

1. Simplify each radical where possible:

   • $\sqrt{45} = \sqrt{9 \cdot 5} = 3\sqrt{5}$
   • $\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}$

   Substituting these simplified forms: [ 4\sqrt{5} + 9(3\sqrt{5}) + 3(2%