Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{\left( {5\sqrt 2 + 2\sqrt 5 } \right).\left( {\sqrt 3 - 3\sqrt 2 } \right)}}{{\sqrt {30} }}\\
= \dfrac{{\left( {{{\sqrt 5 }^2}.\sqrt 2 + {{\sqrt 2 }^2}.\sqrt 5 } \right).\left( {\sqrt 3 - {{\sqrt 3 }^2}.\sqrt 2 } \right)}}{{\sqrt {30} }}\\
= \dfrac{{\sqrt 5 .\sqrt 2 .\left( {\sqrt 5 + \sqrt 2 } \right).\sqrt 3 .\left( {1 - \sqrt 3 .\sqrt 2 } \right)}}{{\sqrt {30} }}\\
= \dfrac{{\sqrt {5.2.3} .\left( {\sqrt 5 + \sqrt 2 } \right).\left( {1 - \sqrt 6 } \right)}}{{\sqrt {30} }}\\
= \dfrac{{\sqrt {30} .\left( {\sqrt 5 - \sqrt {30} + \sqrt 2 - \sqrt {12} } \right)}}{{\sqrt {30} }}\\
= \sqrt 5 - \sqrt {30} + \sqrt 2 - 2\sqrt 3
\end{array}\)
