1. The problem is to simplify the expression $$\sqrt{18x^{4}}$$. 2. Recall the property of square roots: $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$ and that $$\sqrt{x^{2}} = |x|$$. 3. Factor inside the square root: $$18x^{4} = 9 \cdot 2 \cdot x^{4}$$. 4. Apply the square root to each factor: $$\sqrt{9} \cdot \sqrt{2} \cdot \sqrt{x^{4}}$$. 5. Simplify each square root: $$\sqrt{9} = 3$$, $$\sqrt{2}$$ stays as is, and $$\sqrt{x^{4}} = x^{2}$$ because $$\sqrt{x^{4}} = (x^{4})^{\frac{1}{2}} = x^{2}$$. 6. Combine the simplified parts: $$3 \cdot x^{2} \cdot \sqrt{2} = 3x^{2}\sqrt{2}$$. 7. Therefore, the simplified form is $$3x^{2}\sqrt{2}$$. The correct answer is: 3x^{2}\sqrt{2}.