Calculate: 2+sqrt(8)

Expression: $2+\sqrt{ 8 }$

Write the number in exponential form with the base of $2$

$2+\sqrt{ {2}^{3} }$

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 $2$

$\begin{align*}&2+2\sqrt{ 2 } \\&\approx4.82843\end{align*}$