To evaluate the numerical expression [tex]\(\left(2^3\right)^{\frac{1}{2}}\)[/tex], let's follow a step-by-step process:
1. Evaluate the inner exponentiation first:
[tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
2. Now we have the expression [tex]\(\sqrt{8}\)[/tex]:
[tex]\(((2^3)^{\frac{1}{2}} = 8^{\frac{1}{2}} = \sqrt{8})\)[/tex]
3. Convert the radical expression to a numerical value:
[tex]\[
\sqrt{8} = 2.8284271247461903
\][/tex]
Thus, the numerical value of the expression [tex]\(\left(2^3\right)^{\frac{1}{2}}\)[/tex] is approximately [tex]\(2.8284271247461903\)[/tex].
Among the provided options:
- 4
- [tex]\(\sqrt[3]{4}\)[/tex]
- [tex]\(\sqrt{8}\)[/tex]
- [tex]\(\sqrt{128}\)[/tex]
The correct simplified expression that matches the value [tex]\(\sqrt{8}\)[/tex].
