Subtract 1119−−√−519−−√.

Answer 1

We are asked to subtract $\sqrt{1119}-\sqrt{519}$. Let's simplify each square root separately: \begin{align*}
\sqrt{1119} &= \sqrt{111 \cdot 10+9} = \sqrt{111 \cdot 100+9} \approx \sqrt{111 \cdot 100} = \sqrt{11100}\\
\sqrt{519} &= \sqrt{51 \cdot 10+9} = \sqrt{51 \cdot 100+9} \approx \sqrt{51 \cdot 100} = \sqrt{5100}
\end{align*}Therefore, $\sqrt{1119} \approx \sqrt{11100}$ and $\sqrt{519} \approx \sqrt{5100}$. We can estimate $\sqrt{11100}$ as $\sqrt{10000}=100$, since $100^2 = 10000$. Similarly, $\sqrt{5100} \approx \sqrt{5000} = \sqrt{50^2 \cdot 10} = 50\sqrt{10}$. Therefore, $\sqrt{1119}-\sqrt{519} \approx 100-50\sqrt{10} = \boxed{100-50\sqrt{10}}$.