Evaluate: (2+sqrt(3)) * (1+sqrt(3))

Expression: $\left( 2+\sqrt{ 3 } \right) \times \left( 1+\sqrt{ 3 } \right)$

Multiply each term in the first parentheses by each term in the second parentheses (FOIL)

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

When a square root of an expression is multiplied by itself, the result is that expression

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

Add the numbers

$5+2\sqrt{ 3 }+\sqrt{ 3 }$

Collect like terms

$\begin{align*}&5+3\sqrt{ 3 } \\&\approx10.19615\end{align*}$