Question

Lela had to determine the largest of the following real numbers
√30-5, 3√14-6, 6.03, 2π

Answer 1

To find the largest of the values \(\sqrt{30} - 5\), \(3\sqrt{14} - 6\), \(6.03\), and \(2\pi\), we will evaluate each expression.

1. **Calculating \(\sqrt{30} - 5\)**:
\[
\sqrt{30} \approx 5.477 \, (\text{since } 5.477^2 \approx 30)
\]
Thus,
\[
\sqrt{30} - 5 \approx 5.477 - 5 = 0.477
\]

2. **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,
\[
3\sqrt{14} - 6 \approx 11.226 - 6 = 5.226
\]

3. **The value \(6.03\)** is already given.

4. **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:
\[
\boxed{2\pi}
\]