To determine which is greater between [tex]\(\sqrt[3]{3}\)[/tex] (the cube root of 3) and [tex]\(\sqrt[4]{4}\)[/tex] (the fourth root of 4), we can follow these steps:
1. Calculate the cube root of 3:
[tex]\(\sqrt[3]{3}\)[/tex] approximately equals 1.442.
2. Calculate the fourth root of 4:
[tex]\(\sqrt[4]{4}\)[/tex] approximately equals 1.414.
3. Compare the values:
- Cube root of 3 is approximately 1.442.
- Fourth root of 4 is approximately 1.414.
Since 1.442 is greater than 1.414, [tex]\(\sqrt[3]{3}\)[/tex] is greater than [tex]\(\sqrt[4]{4}\)[/tex]. Therefore, [tex]\(\sqrt[3]{3} > \sqrt[4]{4}\)[/tex].
