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To evaluate the expression \(\sqrt{2x^2} \cdot \sqrt{6x}\), let's follow these steps:

### Step 1: Combine the Square Roots
We can combine the square roots into one expression:
\[
\sqrt{2x^2} \cdot \sqrt{6x} = \sqrt{(2x^2) \cdot (6x)}
\]

### Step 2: Multiply the Terms Inside the Square Root
Now, multiply the terms inside the square root:
\[
(2x^2) \cdot (6x) = 12x^3
\]

So the expression becomes:
\[
\sqrt{12x^3}
\]

### Step 3: Simplify the Square Root
Next, simplify the square root:
\[
\sqrt{12x^3} = \sqrt{4 \times 3 \times x^2 \times x} = \sqrt{4} \times \sqrt{x^2} \times \sqrt{3x}
\]

Since \(\sqrt{4} = 2\) and \(\sqrt{x^2} = x\), the expression simplifies to:
\[
2x\sqrt{3x}
\]

### Final Answer:
The evaluated expression is:
\[
2x\sqrt{3x}
\]

Would you like further details or have any questions about this process?

Here are some related questions:
1. What are the rules for multiplying square roots?
2. How do you simplify expressions involving square roots?
3. Can this expression be further simplified for specific values of \(x\)?
4. How would this expression change if \(x\) were negative?
5. What happens if you square the final simplified expression?

**Tip:** When multiplying square roots, always check if the expression can be simplified further by factoring out perfect squares.

Evaluate the expression: √(2x²) · √(6x)

Learn how to evaluate and simplify the expression √(2x²) · √(6x). This detailed step-by-step solution covers the multiplication of square roots and simplifying the final result. Ideal for high school students in Grades 9-11.

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