Question

Order the numbers from greatest to least: (square root of 27 divided by 3; 7/3; square root of 15; 0; negative square root of 45; -0.0123456…)

Answer 1

To order the numbers from greatest to least, we first need to calculate their respective values:

1. **Square root of 27 divided by 3**:
\(\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}\)
Approximately \( \sqrt{3} \approx 1.732\), then:
\( \frac{3\sqrt{3}}{3} = \sqrt{3} \approx 1.732\)

2. **7/3**:
\( \frac{7}{3} \approx 2.333\)

3. **Square root of 15**:
\(\sqrt{15} \approx 3.873\)

4. **0**:
The value is \(0\).

5. **Negative square root of 45**:
\(-\sqrt{45} = -\sqrt{9 \times 5} = -3\sqrt{5}\)
Approximately \( \sqrt{5} \approx 2.236\), then:
\(-3\sqrt{5} \approx -6.708\)

6. **-0.0123456**:
The value is \(-0.0123456\).

Now we arrange these numbers:
- \( \sqrt{27}/3 \approx 1.732\)
- \( 7/3 \approx 2.333\)
- \( \sqrt{15} \approx 3.873\)
- \( 0\)
- \( -\sqrt{45} \approx -6.708\)
- \( -0.0123456\)

Now let's place them from greatest to least:

1. \( \sqrt{15} \approx 3.873\)
2. \( 7/3 \approx 2.333\)
3. \( \sqrt{27}/3 \approx 1.732\)
4. \( 0\)
5. \( -0.0123456\)
6. \( -\sqrt{45} \approx -6.708\)

So, the final order from greatest to least is:
\[
\sqrt{15}, \frac{7}{3}, \frac{\sqrt{27}}{3}, 0, -0.0123456, -\sqrt{45}
\]