می‌دانیم $\left| x \right| = \left\{ \begin{gathered}
  x\,\,\,\,\,\,\,\,\,\,\,\,\,x \geqslant 0 \hfill \\
  x \lt 0 \hfill \\ 
\end{gathered}  \right.$ پس هر قدرمطلق را تعیین علامت می‌کنیم:

$\left| {2\sqrt 3  - 1} \right| \to 2\sqrt 3  = \sqrt {12}  \to \sqrt {12}  \gt 1$ می‌دانیم $ \Rightarrow 2\sqrt 3  - 1 \gt 0$

$\left| {\sqrt 3  - 1} \right| \to \sqrt 3  \gt 1 \Rightarrow \sqrt 3  - 1 \gt 0$

$\left| {1 - \sqrt 3 } \right| \to \sqrt 3  \gt 1 \Rightarrow 1 - \sqrt 3  \lt 0$

$\begin{gathered}
  \underbrace {\left| {2\sqrt 3  - 1} \right|}_ +  + \underbrace {\left| {\sqrt 3  - 1} \right|}_ +  \times \underbrace {\left| {1 - \sqrt 3 } \right|}_ -  = (2\sqrt 3  - 1) + (\sqrt 3  - 1) \times \left( { - (\sqrt 3 )} \right) \hfill \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = (2\sqrt 3  - 1) + (\sqrt 3  - 1) \times (\sqrt 3  - 1) = 2\sqrt 3  - 1 + {(\sqrt 3 )^2} - 2\sqrt 3  + 1 = 3 \hfill \\ 
\end{gathered} $