To solve for the value of [tex]\(\sqrt[3]{2} \cdot \sqrt[3]{32}\)[/tex], we need to calculate each cube root individually and then multiply the results together. Let's go through this step by step:
1. Calculate [tex]\(\sqrt[3]{2}\)[/tex]:
The cube root of 2 is approximately [tex]\(1.2599210498948732\)[/tex].
2. Calculate [tex]\(\sqrt[3]{32}\)[/tex]:
The cube root of 32 is approximately [tex]\(3.1748021039363987\)[/tex].
3. Multiply the two results together:
Now we multiply the cube root of 2 and the cube root of 32:
[tex]\[
\sqrt[3]{2} \cdot \sqrt[3]{32} \approx 1.2599210498948732 \times 3.1748021039363987.
\][/tex]
4. Find the product:
Performing the multiplication, we get:
[tex]\[
1.2599210498948732 \times 3.1748021039363987 \approx 4.0.
\][/tex]
Therefore, the value of [tex]\(\sqrt[3]{2} \cdot \sqrt[3]{32}\)[/tex] is approximately [tex]\(4.0\)[/tex].
