To determine the order of the expressions [tex]\(\sqrt[3]{58}\)[/tex], [tex]\(\frac{32}{7}\)[/tex], and [tex]\(\sqrt{28}\)[/tex] from greatest to least, let’s first evaluate them numerically.
1. Evaluating [tex]\(\sqrt[3]{58}\)[/tex]:
[tex]\[
\sqrt[3]{58} \approx 3.8709
\][/tex]
2. Evaluating [tex]\(\frac{32}{7}\)[/tex]:
[tex]\[
\frac{32}{7} \approx 4.5714
\][/tex]
3. Evaluating [tex]\(\sqrt{28}\)[/tex]:
[tex]\[
\sqrt{28} \approx 5.2915
\][/tex]
With these numerical values, we can compare and order them from greatest to least:
- [tex]\(\sqrt{28} \approx 5.2915\)[/tex]
- [tex]\(\frac{32}{7} \approx 4.5714\)[/tex]
- [tex]\(\sqrt[3]{58} \approx 3.8709\)[/tex]
Thus, the correct order from greatest to least is:
[tex]\[
\sqrt{28}, \frac{32}{7}, \sqrt[3]{58}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\sqrt{28}, \frac{32}{7}, \sqrt[3]{58}}
\][/tex]
