1. The problem is to find the value of $\sqrt{93614.4}$.\n\n2. The square root function $\sqrt{x}$ gives a number which, when multiplied by itself, equals $x$.\n\n3. To find $\sqrt{93614.4}$, we can use a calculator or estimate by finding the square root of a nearby perfect square.\n\n4. Note that $\sqrt{93614.4} = \sqrt{936144 \times 0.1} = \sqrt{936144} \times \sqrt{0.1}$.\n\n5. Calculate $\sqrt{936144}$. Since $967^2 = 935089$ and $968^2 = 936992$, $\sqrt{936144}$ is approximately $967.5$.\n\n6. Calculate $\sqrt{0.1} = \sqrt{\frac{1}{10}} = \frac{1}{\sqrt{10}} \approx 0.3162$.\n\n7. Multiply the two results: $967.5 \times 0.3162 \approx 305.7$.\n\n8. Therefore, $\sqrt{93614.4} \approx 305.7$.