To simplify $\sqrt{20x^2}$:

1. Break down the square root:
   $\sqrt{20x^2} = \sqrt{20} \cdot \sqrt{x^2}$.

2. Simplify each part:

   • $\sqrt{20}$ can be broken down further: $\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}$.
   • $\sqrt{x^2} = x$, assuming $x \geq 0$.

3. Combine the simplified parts:
   $\sqrt{20x^2} = 2\sqrt{5} \cdot x = 2x\sqrt{5}$.

Final Answer:

$\sqrt{20x^2} = 2x\sqrt{5}$

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Do you want further explanations or have any questions? 😊

Related Questions:

1. How do you simplify square roots with higher powers (e.g., $\sqrt{50x^4}$)?
2. What happens if $x$ is negative when simplifying square roots?
3. Can square roots always be simplified to exact forms?
4. What is the difference between a radical and a square root?
5. How do you multiply or divide square roots like $\sqrt{20} \cdot \sqrt{45}$?

Tip:

When simplifying square roots, always look for perfect squares within the number (like $4, 9, 16$)—this makes it easier!