https://file.aiquickdraw.com/mathbot/file/17270435838890ut55zah.jpg

The given expression is:

\[
\sqrt{2x} \cdot \sqrt{10}
\]

### Step-by-step simplification:

1. **Combine the square roots**:
   - Use the property of square roots: \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).
   - Applying this rule, we have:
   \[
   \sqrt{2x} \cdot \sqrt{10} = \sqrt{2x \cdot 10}
   \]

2. **Simplify the product under the square root**:
   - Multiply \(2x \cdot 10\):
   \[
   2x \cdot 10 = 20x
   \]
   So, the expression becomes:
   \[
   \sqrt{20x}
   \]

3. **Simplify \(\sqrt{20x}\)**:
   - Factor 20 as \(4 \times 5\), so:
   \[
   \sqrt{20x} = \sqrt{4 \times 5x} = \sqrt{4} \cdot \sqrt{5x} = 2\sqrt{5x}
   \]

Thus, the simplified expression is \(2\sqrt{5x}\).

### Answer:
The correct option is: **\(2\sqrt{5x}\)**.

Let me know if you'd like further explanation!

Here are some related questions:
1. How do you combine square roots in general?
2. What happens when you have variables inside square roots?
3. How do you simplify square roots with products inside?
4. Can square roots be simplified further if there are higher powers inside?
5. What are other useful properties of square roots?

**Tip**: When simplifying square roots, always check if the number inside the root can be factored to simplify the expression.

Simplify the given expression: \( \sqrt{2x} \cdot \sqrt{10} \)

Learn how to simplify the square root expression \( \sqrt{2x} \cdot \sqrt{10} \) with a detailed step-by-step solution. This problem covers key algebraic concepts and properties of square roots, ideal for students in Grades 9-11.

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