The given expression is:

$\sqrt{80} - 2\sqrt{45}$

Let's simplify each term step by step.

1. Simplifying $\sqrt{80}$

We can factor 80 as:

$80 = 16 \times 5$

Since $\sqrt{16} = 4$, we can simplify:

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

2. Simplifying $2\sqrt{45}$

We can factor 45 as:

$45 = 9 \times 5$

Since $\sqrt{9} = 3$, we can simplify:

$2\sqrt{45} = 2 \times \sqrt{9 \times 5} = 2 \times 3\sqrt{5} = 6\sqrt{5}$

3. Simplifying the whole expression:

Now substitute the simplified forms back into the original expression:

$4\sqrt{5} - 6\sqrt{5}$

Since both terms have $\sqrt{5}$, we can combine them:

$(4 - 6)\sqrt{5} = -2\sqrt{5}$

Final Answer:

The simplified expression is:

$-2\sqrt{5}$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you factor numbers under a square root?
2. What is the rule for simplifying square roots involving multiplication?
3. Can you simplify $\sqrt{50} + \sqrt{18}$?
4. How do you handle coefficients when simplifying square roots?
5. How do negative coefficients affect square root expressions?

Tip: Always check if the number under the square root has a perfect square factor to simplify expressions easily.