Sure, let's evaluate each term step by step precisely:
1. Evaluate \(\sqrt[3]{4} \cdot \sqrt{3}\):
The cube root of 4 (\(\sqrt[3]{4}\)) is approximately 1.587.
The square root of 3 (\(\sqrt{3}\)) is approximately 1.732.
Multiplying these together:
[tex]\[
\sqrt[3]{4} \cdot \sqrt{3} \approx 1.587 \cdot 1.732 = 2.749
\][/tex]
So, \(\sqrt[3]{4} \cdot \sqrt{3}\) is approximately 2.749.
2. Evaluate \(2(\sqrt[6]{9})\):
The sixth root of 9 (\(\sqrt[6]{9}\)) is approximately 1.442.
Multiplying by 2:
[tex]\[
2 \cdot \sqrt[6]{9} \approx 2 \cdot 1.442 = 2.884
\][/tex]
So, \(2(\sqrt[6]{9})\) is approximately 2.884.
3. Evaluate \(\sqrt[6]{12}\):
The sixth root of 12 (\(\sqrt[6]{12}\)) is approximately 1.513.
So, \(\sqrt[6]{12}\) is approximately 1.513.
4. Evaluate \(\sqrt[6]{432}\):
The sixth root of 432 (\(\sqrt[6]{432}\)) is approximately 2.749.
So, \(\sqrt[6]{432}\) is approximately 2.749.
5. Evaluate \(2(\sqrt[6]{3.888})\):
The sixth root of 3.888 (\(\sqrt[6]{3.888}\)) is approximately 1.254.
Multiplying by 2:
[tex]\[
2 \cdot \sqrt[6]{3.888} \approx 2 \cdot 1.254 = 2.508
\][/tex]
So, \(2(\sqrt[6]{3.888})\) is approximately 2.508.
Therefore, the results for the terms are:
1. \(\sqrt[3]{4} \cdot \sqrt{3}\) is approximately 2.749.
2. \(2(\sqrt[6]{9})\) is approximately 2.884.
3. \(\sqrt[6]{12}\) is approximately 1.513.
4. \(\sqrt[6]{432}\) is approximately 2.749.
5. \(2(\sqrt[6]{3.888})\) is approximately 2.508.
Thus, the computations for each term yield:
[tex]\[
(2.749, 2.884, 1.513, 2.749, 2.508)
\][/tex]
