Question
8. Order the numbers from greatest to least. \begin{tabular}{|l}\( \equiv-\sqrt{12} \) \\ \( \equiv \sqrt{15} \) \\ \( \equiv-4.3 \) \\ \( \equiv \frac{14}{5} \) \\ \( \equiv 3 \)\end{tabular}
Ask by Higgins Cole. in the United States
Jan 17,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The numbers ordered from greatest to least are:
\[
\sqrt{15}, \quad 3, \quad \frac{14}{5}, \quad -\sqrt{12}, \quad -4.3
\]
Solution
To order the given numbers from greatest to least, let's first evaluate each number:
1. **\(-\sqrt{12}\)**
\[
\sqrt{12} \approx 3.464 \\
-\sqrt{12} \approx -3.464
\]
2. **\(\sqrt{15}\)**
\[
\sqrt{15} \approx 3.873
\]
3. **\(-4.3\)**
\[
-4.3 \text{ is already in decimal form.}
\]
4. **\(\frac{14}{5}\)**
\[
\frac{14}{5} = 2.8
\]
5. **\(3\)**
\[
3 \text{ is already in decimal form.}
\]
Now, let's list the numbers with their approximate decimal values:
- \(\sqrt{15} \approx 3.873\)
- \(3 = 3.0\)
- \(\frac{14}{5} = 2.8\)
- \(-\sqrt{12} \approx -3.464\)
- \(-4.3 = -4.3\)
**Ordered from Greatest to Least:**
1. \(\sqrt{15}\) ≈ **3.873**
2. \(3\) ≈ **3.0**
3. \(\frac{14}{5}\) = **2.8**
4. \(-\sqrt{12}\) ≈ **-3.464**
5. \(-4.3\) = **-4.3**
**Final Order:**
\[
\sqrt{15}, \quad 3, \quad \frac{14}{5}, \quad -\sqrt{12}, \quad -4.3
\]
Reviewed and approved by the UpStudy tutoring team
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Extra Insights
To order the numbers from greatest to least, let's first convert the expressions into decimal form or approximate them: 1. \( \equiv -\sqrt{12} \approx -3.46 \) 2. \( \equiv \sqrt{15} \approx 3.87 \) 3. \( \equiv -4.3 = -4.3 \) 4. \( \equiv \frac{14}{5} = 2.8 \) 5. \( \equiv 3 = 3 \) Now ordering these from greatest to least: 1. \( \sqrt{15} \approx 3.87 \) 2. \( 3 \) 3. \( \frac{14}{5} = 2.8 \) 4. \( -\sqrt{12} \approx -3.46 \) 5. \( -4.3 \) So, the complete ordered list is: \( \sqrt{15}, 3, \frac{14}{5}, -\sqrt{12}, -4.3 \).