https://file.aiquickdraw.com/mathbot/file/1727966082166972a59l1.jpg

The expression given in the image is \( 5 \sqrt{80a^2} \).

Let's simplify it step by step:

1. Break down the square root:
   \[
   \sqrt{80a^2} = \sqrt{80} \cdot \sqrt{a^2}
   \]
   
2. Simplify the square root of \( a^2 \):
   \[
   \sqrt{a^2} = a
   \]

3. Now, simplify \( \sqrt{80} \). We can factor \( 80 \) as \( 16 \times 5 \), and then use the property of square roots:
   \[
   \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4 \sqrt{5}
   \]

4. Putting it all together:
   \[
   \sqrt{80a^2} = 4a\sqrt{5}
   \]

5. Multiply by the 5 outside the square root:
   \[
   5 \times 4a\sqrt{5} = 20a\sqrt{5}
   \]

So, the simplified form of \( 5 \sqrt{80a^2} \) is:
\[
20a\sqrt{5}
\]

Let me know if you'd like further details or explanations!

Here are five related questions to extend your understanding:
1. How would you simplify \( \sqrt{45a^2} \)?
2. What is the simplified form of \( 3 \sqrt{50b^4} \)?
3. How can you express \( \sqrt{100x^6} \)?
4. What steps would you take to simplify \( 6 \sqrt{72a^3b^2} \)?
5. Can you find the simplified expression for \( 2 \sqrt{180a^2} \)?

**Tip:** When simplifying square roots, always look for perfect squares that are factors of the number under the root to break them down efficiently.

Learn how to simplify the expression 5√80a^2 with this detailed, step-by-step explanation. This problem covers key algebraic concepts, including simplifying square roots and radicals, and is suitable for students in Grades 8-10.

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