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Which is greater, [tex]\sqrt[3]{3}[/tex] or [tex]\sqrt[4]{4}[/tex]?

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GinnyAnswer
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].
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