The problem is to simplify the expression $\sqrt{320} - \sqrt{80} + \sqrt{75} + \sqrt{9}$.

1. Problem Description

The problem is to simplify the expression $\sqrt{320} - \sqrt{80} + \sqrt{75} + \sqrt{9}$.

2. Solution Steps

First, we simplify each square root:

$\sqrt{320} = \sqrt{64 \cdot 5} = \sqrt{64} \cdot \sqrt{5} = 8\sqrt{5}$

$\sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5}$

$\sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3}$

$\sqrt{9} = 3$

Now we substitute these simplified expressions back into the original expression:

$8\sqrt{5} - 4\sqrt{5} + 5\sqrt{3} + 3$

Combine like terms:

$(8\sqrt{5} - 4\sqrt{5}) + 5\sqrt{3} + 3$

$4\sqrt{5} + 5\sqrt{3} + 3$

3. Final Answer

$3 + 4\sqrt{5} + 5\sqrt{3}$