1. **State the problem:** Simplify the expression $9x^2(5-\sqrt{x})$. 2. **Recall the distributive property:** To simplify expressions like this, multiply $9x^2$ by each term inside the parentheses separately. 3. **Apply the distributive property:** $$9x^2 \times 5 - 9x^2 \times \sqrt{x}$$ 4. **Multiply the terms:** $$45x^2 - 9x^2 \sqrt{x}$$ 5. **Simplify the second term:** Recall that $\sqrt{x} = x^{\frac{1}{2}}$, so $$9x^2 \sqrt{x} = 9x^2 x^{\frac{1}{2}} = 9x^{2 + \frac{1}{2}} = 9x^{\frac{5}{2}}$$ 6. **Write the final simplified expression:** $$45x^2 - 9x^{\frac{5}{2}}$$ This is the simplified form of the original expression.