Rút gọn \( {P = \sqrt {6 + \sqrt 8 + \sqrt {12} + \sqrt {24} } }\)

* Hướng dẫn giải

 \(\begin{array}{*{20}{l}} {P = \sqrt {6 + \sqrt 8 + \sqrt {12} + \sqrt {24} } }\\ { = \sqrt {6 + \sqrt {4.2} + \sqrt {4.3} + \sqrt {4.6} } }\\ { = \sqrt {6 + 2\sqrt 2 + 2\sqrt 3 + 2\sqrt 6 } }\\ { = \sqrt {2 + 3 + 1 + 2\sqrt 2 + 2\sqrt 3 + 2\sqrt 2 .\sqrt 3 } }\\ { = \sqrt {{{\left( {\sqrt 2 + \sqrt 3 + 1} \right)}^2}} }\\ { = \left| {\sqrt 2 + \sqrt 3 + 1} \right|}\\ { = \sqrt 2 + \sqrt 3 + 1{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} } \end{array}\)

\( {{\mkern 1mu} \left( {do{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \sqrt 2 + \sqrt 3 + 1 > 0} \right).}\)