https://file.aiquickdraw.com/mathbot/file/17274456754265wojgcn8.jpg

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.

Learn how to simplify the expression √80 - 2√45 with a detailed step-by-step solution. This problem involves key mathematical concepts such as factorization, square roots, and simplification techniques. Suitable for students in Grades 9-10.

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