Answer: C: \(2\sqrt{2}\).
Explanation:
To evaluate the numerical expression \((2^3)^{1/2}\), you first calculate the exponent inside the parentheses and then apply the outer exponent.
First, calculate \(2^3\):
\(2^3 = 2 \cdot 2 \cdot 2 = 8\)
Now, apply the outer exponent, which is \(1/2\):
\((8)^{1/2}\)
Taking the square root of 8, we get:
\(\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}\)
So, the correct answer is option C: \(2\sqrt{2}\).