To find the value of \( \sqrt{1119} - \sqrt{519} \), we can first calculate the square roots separately and then subtract them.
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Calculate \( \sqrt{1119} \):
- Approximate value: \( \sqrt{1119} \approx 33.45 \)
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Calculate \( \sqrt{519} \):
- Approximate value: \( \sqrt{519} \approx 22.8 \)
Now subtract the two values: \[ \sqrt{1119} - \sqrt{519} \approx 33.45 - 22.8 = 10.65 \]
Therefore, the difference is approximately \( \boxed{10.65} \).