The problem asks for the simplified form of:

$2 \sqrt{5} + 3 \sqrt{45} - 2 \sqrt{80}$

Let's simplify each term one by one:

1. $\sqrt{45}$ can be broken down as: $\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3 \sqrt{5}$ Therefore, $3 \sqrt{45} = 3 \times 3 \sqrt{5} = 9 \sqrt{5}$.

2. $\sqrt{80}$ can be simplified as: $\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4 \sqrt{5}$ Therefore, $2 \sqrt{80} = 2 \times 4 \sqrt{5} = 8 \sqrt{5}$.

Now, substitute the simplified terms back into the original expression:

$2 \sqrt{5} + 9 \sqrt{5} - 8 \sqrt{5}$

Combine the terms with $\sqrt{5}$:

$(2 + 9 - 8) \sqrt{5} = 3 \sqrt{5}$

Thus, the simplified form is $3 \sqrt{5}$.

The correct answer is B. $3 \sqrt{5}$.

Do you need further explanation or details on any step?

Here are some related questions:

1. How do you simplify square roots involving multiplication?
2. What are the properties of square roots in algebraic expressions?
3. How can you combine terms with the same radical?
4. Can you always simplify square roots like $\sqrt{45}$?
5. How do you factor numbers to simplify square roots more easily?

Tip: When simplifying square roots, always look for perfect squares as factors. This makes the process much quicker!