To determine the order of the numbers [tex]\(\sqrt{28}\)[/tex], [tex]\(\frac{32}{7}\)[/tex], and [tex]\(\sqrt[3]{58}\)[/tex] from greatest to least, we need to calculate each of these values.
1. Calculate [tex]\(\sqrt{28}\)[/tex]:
[tex]\[
\sqrt{28} \approx 5.291502622129181
\][/tex]
2. Calculate [tex]\(\frac{32}{7}\)[/tex]:
[tex]\[
\frac{32}{7} \approx 4.571428571428571
\][/tex]
3. Calculate [tex]\(\sqrt[3]{58}\)[/tex]:
[tex]\[
\sqrt[3]{58} \approx 3.870876640627797
\][/tex]
Now, we need to arrange these values in descending order. Comparing the calculated values:
- [tex]\(\sqrt{28} \approx 5.291502622129181\)[/tex]
- [tex]\(\frac{32}{7} \approx 4.571428571428571\)[/tex]
- [tex]\(\sqrt[3]{58} \approx 3.870876640627797\)[/tex]
Ordering these from greatest to least, we get:
[tex]\[ \sqrt{28}, \frac{32}{7}, \sqrt[3]{58} \][/tex]
So, the correct answer is:
[tex]\[ \sqrt{28}, \frac{32}{7}, \sqrt[3]{58} \][/tex]
Hence, the order from greatest to least is:
[tex]\[
\boxed{\sqrt{28}, \frac{32}{7}, \sqrt[3]{58}}
\][/tex]
