1. **State the problem:** Write the expression $\sqrt{75x^{20}}$ in radical form assuming $x>0$. 2. **Recall the formula:** The square root of a product is the product of the square roots: $$\sqrt{ab} = \sqrt{a} \times \sqrt{b}$$ 3. **Apply the formula:** $$\sqrt{75x^{20}} = \sqrt{75} \times \sqrt{x^{20}}$$ 4. **Simplify each part:** - Factor 75 as $75 = 25 \times 3$. - So, $$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$$ - For $\sqrt{x^{20}}$, since $x>0$, $$\sqrt{x^{20}} = x^{\frac{20}{2}} = x^{10}$$ 5. **Combine the simplified parts:** $$\sqrt{75x^{20}} = 5\sqrt{3} \times x^{10} = 5x^{10}\sqrt{3}$$ **Final answer:** $$\boxed{5x^{10}\sqrt{3}}$$