Question

Put these numbers in order from least to greatest: -√124, -3√17, -6pi

Answer 1

To compare the numbers \(-\sqrt{124}\), \(-3\sqrt{17}\), and \(-6\pi\), we will first calculate their approximate values.

1. \(-\sqrt{124}\):
- \(\sqrt{124} \approx 11.13\) (since \(11^2 = 121\) and \(12^2 = 144\)),
- Therefore, \(-\sqrt{124} \approx -11.13\).

2. \(-3\sqrt{17}\):
- \(\sqrt{17} \approx 4.12\) (since \(4^2 = 16\) and \(5^2 = 25\)),
- So, \(-3\sqrt{17} \approx -3 \times 4.12 = -12.36\).

3. \(-6\pi\):
- \(\pi \approx 3.14\),
- Thus, \(-6\pi \approx -6 \times 3.14 \approx -18.84\).

Now we have the approximate values:
- \(-\sqrt{124} \approx -11.13\)
- \(-3\sqrt{17} \approx -12.36\)
- \(-6\pi \approx -18.84\)

Now we can place these values in order from least to greatest:
\(-6\pi < -3\sqrt{17} < -\sqrt{124}\).

Thus, the ordered list from least to greatest is:
\[
-6\pi, -3\sqrt{17}, -\sqrt{124}.
\]