Order [tex]\sqrt[3]{58}, \frac{32}{7}, \sqrt{28}[/tex] from greatest to least:

A. [tex]\sqrt{28}, \frac{32}{7}, \sqrt[3]{58}[/tex]
B. [tex]\frac{32}{7}, \sqrt{28}, \sqrt[3]{58}[/tex]
C. [tex]\sqrt[3]{58}, \sqrt{28}, \frac{32}{7}[/tex]
D. [tex]\frac{32}{7}, \sqrt[3]{58}, \sqrt{28}[/tex]



Answer :

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]