1. **State the problem:** Multiply $$\sqrt{14p^5} \cdot \sqrt{3}$$ assuming $$p \geq 0$$ and simplify the result. 2. **Use the property of square roots:** $$\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$$. 3. **Apply this property:** $$\sqrt{14p^5} \cdot \sqrt{3} = \sqrt{14p^5 \cdot 3} = \sqrt{42p^5}$$ 4. **Simplify the square root:** Since $$p \geq 0$$, we can write $$p^5 = p^4 \cdot p = (p^2)^2 \cdot p$$. 5. **Extract perfect squares from the square root:** $$\sqrt{42p^5} = \sqrt{42 \cdot p^4 \cdot p} = \sqrt{42} \cdot \sqrt{p^4} \cdot \sqrt{p} = \sqrt{42} \cdot p^2 \cdot \sqrt{p}$$ 6. **Write the final simplified form:** $$p^2 \sqrt{42p}$$ **Final answer:** $$p^2 \sqrt{42p}$$