1. Problem: Simplify the expression $$\sqrt{8x} \cdot \sqrt{4x} \cdot \sqrt{3x}$$. 2. Formula: Recall that $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$$ for any non-negative $a,b$. 3. Apply the formula: $$\sqrt{8x} \cdot \sqrt{4x} \cdot \sqrt{3x} = \sqrt{8x \cdot 4x \cdot 3x}$$ 4. Multiply inside the radical: $$8x \cdot 4x \cdot 3x = (8 \cdot 4 \cdot 3) \cdot (x \cdot x \cdot x) = 96x^3$$ 5. So the expression becomes: $$\sqrt{96x^3}$$ 6. Simplify the radical by factoring: $$96 = 16 \times 6$$ and $$x^3 = x^2 \cdot x$$, so $$\sqrt{96x^3} = \sqrt{16 \times 6 \times x^2 \times x} = \sqrt{16} \cdot \sqrt{6} \cdot \sqrt{x^2} \cdot \sqrt{x}$$ 7. Evaluate the perfect squares: $$\sqrt{16} = 4$$ and $$\sqrt{x^2} = x$$ 8. Final simplified form: $$4x \sqrt{6x}$$ Answer: $$4x \sqrt{6x}$$