Rút gọn A = (căn bậc hai (căn bậc hai 7 - căn bậc hai 3) - căn bậc hai (căn bậc hai 7

Ta có:

\[\begin{array}{l}\sqrt {\sqrt 7 - 2} > 0\\\sqrt {\sqrt 7 - \sqrt 3 } < \sqrt {\sqrt 7 + \sqrt 3 } \Leftrightarrow \sqrt {\sqrt 7 - \sqrt 3 } - \sqrt {\sqrt 7 + \sqrt 3 } < 0\\ \Rightarrow A < 0\end{array}\]

Xét \[{{\rm{A}}^2} = {\left( {\frac{{\sqrt {\sqrt 7 - \sqrt 3 } - \sqrt {\sqrt 7 + \sqrt 3 } }}{{\sqrt {\sqrt 7 - 2} }}} \right)^2}\]

\[{{\rm{A}}^2} = \frac{{\sqrt 7 - \sqrt 3 + \sqrt 7 + \sqrt 3 - 2\sqrt {\left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 7 + \sqrt 3 } \right)} }}{{\sqrt 7 - 2}}\]

\[{{\rm{A}}^2} = \frac{{2\sqrt 7 - 2\sqrt 4 }}{{\sqrt 7 - 2}}\]

\[{{\rm{A}}^2} = \frac{{2\sqrt 7 - 2\sqrt 4 }}{{\sqrt 7 - 2}} = \frac{{2\left( {\sqrt 7 - 2} \right)}}{{\sqrt 7 - 2}} = 2\]

Mà A < 0 nên \[{\rm{A}} = - \sqrt 2 \]

Vậy \[{\rm{A}} = - \sqrt 2 \].