Certainly! Let's solve the given expression step by step.
The given expression is:
[tex]\[ \sqrt[3]{2} \cdot \sqrt[3]{32} \][/tex]
### Step-by-Step Solution:
1. Understand the Cube Roots:
- The cube root of a number [tex]\( x \)[/tex], written as [tex]\( \sqrt[3]{x} \)[/tex], is the number [tex]\( y \)[/tex] such that [tex]\( y^3 = x \)[/tex].
2. Calculate [tex]\(\sqrt[3]{2}\)[/tex]:
- The cube root of 2, [tex]\( \sqrt[3]{2} \)[/tex], is approximately [tex]\( 1.2599210498948732 \)[/tex].
3. Calculate [tex]\(\sqrt[3]{32}\)[/tex]:
- The cube root of 32, [tex]\( \sqrt[3]{32} \)[/tex], is approximately [tex]\( 3.1748021039363987 \)[/tex].
4. Multiply the Cube Roots:
- Now, multiply the two cube roots:
[tex]\[ \sqrt[3]{2} \times \sqrt[3]{32} \][/tex]
[tex]\[ 1.2599210498948732 \times 3.1748021039363987 \][/tex]
[tex]\[ \approx 4.0 \][/tex]
### Conclusion:
Thus, the result of the expression [tex]\( \sqrt[3]{2} \cdot \sqrt[3]{32} \)[/tex] is [tex]\( 4.0 \)[/tex].
