To simplify the given radical expression $\sqrt{50x^2}$, let’s break it down step by step:

Step 1: Factor the radicand

The radicand $50x^2$ can be factored into: $50x^2 = 25 \cdot 2 \cdot x^2$

Step 2: Apply the square root property

Using the property $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$, we get: $\sqrt{50x^2} = \sqrt{25} \cdot \sqrt{2} \cdot \sqrt{x^2}$

Step 3: Simplify each square root

$\sqrt{25} = 5, \quad \sqrt{x^2} = x, \quad \sqrt{2} \text{ remains as it is.}$ So: $\sqrt{50x^2} = 5x\sqrt{2}$

Final Answer:

The simplified radical expression is: $5x\sqrt{2}$ This corresponds to option B.

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Do you want more details or have any questions?

Here are 5 related questions to explore:

1. How do you simplify radicals with higher powers of variables, such as $\sqrt{50x^6}$?
2. What are some common mistakes to avoid when simplifying radicals?
3. How does the square root property apply to negative numbers?
4. How do you rationalize the denominator in an expression like $\frac{1}{\sqrt{50x^2}}$?
5. How do you expand an expression like $(\sqrt{50x^2})^2$?

Tip:

Always check if a radicand can be factored into perfect squares to simplify the radical efficiently!