1. **State the problem:** Given $x=111$ and $y=\sqrt{x}$, find the value of $x^2 y$. 2. **Recall the formulas:** - $y = \sqrt{x}$ means $y = x^{1/2}$. - We want to find $x^2 y = x^2 \times x^{1/2}$. 3. **Use exponent rules:** When multiplying powers with the same base, add the exponents: $$x^2 \times x^{1/2} = x^{2 + 1/2} = x^{5/2}$$ 4. **Calculate the value:** $$x^{5/2} = (111)^{5/2} = \left(111^{1/2}\right)^5 = (\sqrt{111})^5$$ 5. **Evaluate $\sqrt{111}$:** $$\sqrt{111} \approx 10.5357$$ 6. **Raise to the 5th power:** $$10.5357^5 \approx 127,628.156$$ **Final answer:** $$x^2 y = 127,628.156$$