1. The problem is to find the square root of 100000. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. We use the formula $\sqrt{x}$ to find the square root. 4. Calculate $\sqrt{100000}$. 5. Express 100000 as $10^5$. 6. Use the property $\sqrt{a^b} = a^{\frac{b}{2}}$. 7. So, $\sqrt{10^5} = 10^{\frac{5}{2}} = 10^{2.5} = 10^2 \times 10^{0.5} = 100 \times \sqrt{10}$. 8. The approximate value of $\sqrt{10}$ is about 3.162. 9. Therefore, $\sqrt{100000} \approx 100 \times 3.162 = 316.2$. 10. Final answer: $\boxed{316.2}$.