1. The problem is to find the square root of 100066.706. 2. The square root function is defined as $\sqrt{x}$, which gives a number $y$ such that $y^2 = x$. 3. To approximate $\sqrt{100066.706}$, note that $100000$ is close and $\sqrt{100000} = 316.2277$ approximately. 4. Since 100066.706 is slightly larger than 100000, its square root will be slightly larger than 316.2277. 5. Using a calculator or approximation method, $\sqrt{100066.706} \approx 316.335$. 6. Therefore, the square root of 100066.706 is approximately $316.335$.