To order the numbers [tex]\(\sqrt[3]{88}\)[/tex], [tex]\(\frac{28}{9}\)[/tex], and [tex]\(\sqrt{19}\)[/tex] from greatest to least, we need to compute the approximate values of each expression.
1. First, let's find the cube root of 88:
[tex]\[\sqrt[3]{88} \approx 4.448\][/tex]
2. Next, let's calculate the value of [tex]\(\frac{28}{9}\)[/tex]:
[tex]\[\frac{28}{9} \approx 3.111\][/tex]
3. Finally, let's find the square root of 19:
[tex]\[\sqrt{19} \approx 4.359\][/tex]
Now, to order these values from greatest to least:
[tex]\[
4.448 \quad (\sqrt[3]{88}), \quad 4.359 \quad (\sqrt{19}), \quad 3.111 \quad (\frac{28}{9})
\][/tex]
Hence, the correct order from greatest to least is:
[tex]\[
\sqrt[3]{88}, \sqrt{19}, \frac{28}{9}
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{\sqrt[3]{88}, \sqrt{19}, \frac{28}{9}}
\][/tex]
