$2+\sqrt{ {2}^{3} }$
Rewrite the exponent as a sum where one of the addends is a multiple of the index$2+\sqrt{ {2}^{2+1} }$
Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression$2+\sqrt{ {2}^{2} \times {2}^{1} }$
Any expression raised to the power of $1$ equals itself$2+\sqrt{ {2}^{2} \times 2 }$
The root of a product is equal to the product of the roots of each factor$2+\sqrt{ {2}^{2} }\sqrt{ 2 }$
Reduce the index of the radical and exponent with $2$$\begin{align*}&2+2\sqrt{ 2 } \\&\approx4.82843\end{align*}$