Question

Put these numbers in order from least to greatest.
-\sqrt{140}
-14.\sqrt{76}
12.7

Answer 1

To order the numbers \(-\sqrt{140}\), \(-14\sqrt{76}\), and \(12.7\) from least to greatest, we first need to evaluate \(-\sqrt{140}\) and \(-14\sqrt{76}\).

1. **Calculate \(-\sqrt{140}\)**:
\[
\sqrt{140} \approx 11.83 \quad (\text{since } 11.83^2 \approx 140)
\]
Therefore,
\[
-\sqrt{140} \approx -11.83
\]

2. **Calculate \(-14\sqrt{76}\)**:
\[
\sqrt{76} \approx 8.72 \quad (\text{since } 8.72^2 \approx 76)
\]
Thus,
\[
-14\sqrt{76} \approx -14 \times 8.72 \approx -121.08
\]

Now we have:
- \(-\sqrt{140} \approx -11.83\)
- \(-14\sqrt{76} \approx -121.08\)
- \(12.7\)

Now we can put these values in order from least to greatest:
\[
-14\sqrt{76} < -\sqrt{140} < 12.7
\]

Therefore, the final order from least to greatest is:
\[
-14\sqrt{76}, -\sqrt{140}, 12.7
\]