Subtract 1119−−√−519−−√.
To subtract √1119 from √519, you can follow these steps:
Step 1: Calculate the square root of 1119:
√1119 ≈ 33.469
Step 2: Calculate the square root of 519:
√519 ≈ 22.782
Step 3: Subtract the two square roots:
33.469 - 22.782 ≈ 10.687
Therefore, the result of subtracting √1119 from √519 is approximately 10.687.
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, $\sqrt{1119}-\sqrt{519} \approx 100-50\sqrt{10} = \boxed{100-50\sqrt{10}}$.
To subtract √1119 - √519, we can follow these steps:
Step 1: Simplify the square roots
√1119 can be simplified as follows: √1119 = √(111 * 10 + 9) = √(111 * 10) + √9 = √111 * √10 + 3√10 = 3√111 + 3√10
Similarly, √519 can be simplified as follows: √519 = √(51 * 10 + 9) = √(51 * 10) + √9 = √51 * √10 + 3√10 = 3√51 + 3√10
Step 2: Perform the subtraction
(3√111 + 3√10) - (3√51 + 3√10)
Since the √10 terms cancel out, the expression simplifies further:
3√111 - 3√51
Therefore, the subtraction of √1119 - √519 is 3√111 - 3√51.