1. The problem is to simplify the expression $$\sqrt{25x^3}$$ assuming $$x > 0$$. 2. Recall the property of square roots: $$\sqrt{ab} = \sqrt{a} \times \sqrt{b}$$. 3. Apply this property to separate the square root: $$\sqrt{25x^3} = \sqrt{25} \times \sqrt{x^3}$$ 4. Simplify $$\sqrt{25}$$ since 25 is a perfect square: $$\sqrt{25} = 5$$ 5. For $$\sqrt{x^3}$$, rewrite the exponent: $$x^3 = x^2 \times x$$ 6. Use the property of square roots again: $$\sqrt{x^3} = \sqrt{x^2 \times x} = \sqrt{x^2} \times \sqrt{x}$$ 7. Simplify $$\sqrt{x^2}$$: $$\sqrt{x^2} = x$$ (since $$x > 0$$) 8. Combine the simplified parts: $$5 \times x \times \sqrt{x} = 5x\sqrt{x}$$ 9. Therefore, the simplest radical form of $$\sqrt{25x^3}$$ is: $$\boxed{5x\sqrt{x}}$$