To evaluate the numerical expression [tex]\(\left(2^3\right)^{\frac{1}{2}}\)[/tex], we need to follow a step-by-step approach:
1. Evaluate the inner exponent first:
[tex]\[
2^3
\][/tex]
[tex]\(2^3\)[/tex] means [tex]\(2\)[/tex] raised to the power [tex]\(3\)[/tex]:
[tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
2. Now, take the square root of the result:
We need to take the square root of [tex]\(8\)[/tex]:
[tex]\[
\sqrt{8}
\][/tex]
The square root of [tex]\(8\)[/tex] can also be written in exponential form as:
[tex]\[
8^{\frac{1}{2}}
\][/tex]
3. Find the value of [tex]\(8^{\frac{1}{2}}\)[/tex]:
The numerical value of the square root of [tex]\(8\)[/tex] is approximately:
[tex]\[
\sqrt{8} \approx 2.8284271247461903
\][/tex]
So, the expression [tex]\(\left(2^3\right)^{\frac{1}{2}}\)[/tex] simplifies to [tex]\(\sqrt{8}\)[/tex], which is approximately [tex]\(2.8284271247461903\)[/tex].
Therefore, the correct answer is:
[tex]\[
\sqrt{8}
\][/tex]
