To find the largest of the values \(\sqrt{30} - 5\), \(3\sqrt{14} - 6\), \(6.03\), and \(2\pi\), we will evaluate each expression.
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Calculating \(\sqrt{30} - 5\): \[ \sqrt{30} \approx 5.477 , (\text{since } 5.477^2 \approx 30) \] Thus, \[ \sqrt{30} - 5 \approx 5.477 - 5 = 0.477 \]
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Calculating \(3\sqrt{14} - 6\): \[ \sqrt{14} \approx 3.742 , (\text{since } 3.742^2 \approx 14) \] Therefore, \[ 3\sqrt{14} \approx 3 \times 3.742 = 11.226 \] Hence, \[ 3\sqrt{14} - 6 \approx 11.226 - 6 = 5.226 \]
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The value \(6.03\) is already given.
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Calculating \(2\pi\): \[ \pi \approx 3.14 \implies 2\pi \approx 2 \times 3.14 = 6.28 \]
Now, we have the approximated values:
- \(\sqrt{30} - 5 \approx 0.477\)
- \(3\sqrt{14} - 6 \approx 5.226\)
- \(6.03\)
- \(2\pi \approx 6.28\)
Comparing the values:
- \(0.477\)
- \(5.226\)
- \(6.03\)
- \(6.28\)
The largest of these numbers is \(2\pi\) which is approximately \(6.28\).
Thus, the largest number is: \[ \boxed{2\pi} \]